practico 1 series
1.0.0
工程师 Mollo 介绍的实用计算系列。
练习1、2、3、4。生成 n...项的算术运算表：
Public Function SelectTable(n As Double , operatorString As String ) As String
Dim result, symbol As String
Dim index As Integer
Dim res As Double
result = "" : symbol = ""
For index = 0 To 10
Select Case operatorString
Case "*"
symbol = " *"
res = (index * n)
Case "/"
symbol = " /"
res = (index / n)
Case "+"
symbol = " +"
res = (index + n)
Case "-"
symbol = " -"
res = (index - n)
End Select
result = result + Str(index) + symbol + Str(n) + " = " + Str(res) + Chr( 13 ) + Chr( 10 )
Next
Return result
End Function # Output: SelectTable(TextBox1.Text, "+")
0 + 5 = 5
1 + 5 = 6
2 + 5 = 7
3 + 5 = 8
4 + 5 = 9
5 + 5 = 10
6 + 5 = 11
7 + 5 = 12
8 + 5 = 13
9 + 5 = 14
10 + 5 = 15
添加 n 项的常规序列：
Public Function RegularSerie(n As UInt16, initialValue As Single , razon As Single , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As UInt32
Dim t, total As Single
For index = 1 To n
t = initialValue + (index - 1 ) * razon
If sumTotal Then
total += t
result = Str(total)
Else
If index = n Then
result += Str(t)
Else
result = result + Str(t) + " + "
End If
End If
Next
Return "F = " + result
End Function # Output: RegularSerie(TextBox1.Text, TextBox2.Text, TextBox3.Text, True)
F = 30
# Output string: RegularSerie(TextBox1.Text, TextBox2.Text, TextBox3.Text, False)
F = 2 + 4 + 6 + 8 + 10
F = (ln(10)+1)/1.7 + (ln(100)+2)/1.9... Log10 参数正在相乘。 X10, X10,..使用乘法累加器。
Public Function LogarithmSerie(n As Integer , initialValue As Double , razon As Double , arg As Double , sumTotal As Boolean ) As String
Dim result As String = ""
Dim count As Double
Dim index As Integer
Dim t, f, total As Double
count = arg
t = initialValue
For index = 1 To n
If sumTotal Then
f = (Math.Log10(count) + index) / t
total += f
result = Str(total)
Else
If index.Equals(n) Then
result = result + "(ln(" + Str(count) + ")+" + Str(index) + ")/" + Str(t)
Else
result = result + "(ln(" + Str(count) + ")+" + Str(index) + ")/" + Str(t) + "+ "
End If
End If
count *= 10
t = Math.Round(t + razon, 2 )
Next
Return "F = " + result
End Function # Output: LogarithmSerie(TextBox1.Text, vi, r, arg, True)
F = 13.617137472838102
# Output string: LogarithmSerie(TextBox1.Text, vi, r, arg, False)
F = (ln(10)+1)/1.7 + (ln(100)+ 2)/ 1.9 + (ln(1000)+3)/2.1 + (ln(10000)+4)/2.3 + (ln(100000)+5)/2.5
F = 100/1 + 99/2 + 97/4...分子将项减少1,2,3...而分母增加1,2,3...，它必须有初始值分子VIN=100，分母VID=1。
Public Function IncreaseAndDecrease(n As Integer , initialValueNumerator As Integer , initialValueDenominator As Integer , isSumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim f, total As Double
For index = 1 To n
If isSumTotal Then
f = (initialValueNumerator / initialValueDenominator)
total += f
result = Str(total)
Else
If index = n Then
result = result + Str(initialValueNumerator) + "/" + Str(initialValueDenominator)
Else
result = result + Str(initialValueNumerator) + "/" + Str(initialValueDenominator) + " + "
End If
End If
initialValueNumerator -= index
initialValueDenominator += index
Next
Return "F =" + result
End Function # Output: IncreaseAndDecrease(TextBox1.Text, TextBox2.Text, TextBox3.Text, True)
F = 195.3603896103896
# Output string: IncreaseAndDecrease(TextBox1.Text, TextBox2.Text, TextBox3.Text, False)
F = 100/ 1 + 99/ 2 + 97/ 4 + 94/ 7 + 90/ 11
F = 5.25/0!+0 + 5.24/1!+1 + 5.22/2!+2...两个元素都是正则级数，分母只需调用阶乘函数即可，当然你必须学会这样做考试的算法。
Public Function Factorial(number As Double ) As Double
Dim fac As Double
Dim index As Integer
If number <> 0 Then
fac = 1
For index = Math.Abs(number) To 1 Step - 1
fac *= index
Next
If number < 0 Then
fac = -fac
End If
Else
fac = 1
End If
Return fac
End Function
Public Function RegularSerieWithFactorial(n As Integer , initialValueNum As Double , initialValueDen As Double , sumTotal As Double ) As String
Dim result As String = ""
Dim index As Integer
Dim t, f, total As Double
For index = 0 To n
If sumTotal Then
If initialValueDen = 0 Then
f = 0
Else
f = initialValueNum / (Factorial(initialValueDen) + initialValueDen)
End If
total += f
result = Str(total)
Else
t = index + 1
If index = n Then
result = result + Str(Math.Round(initialValueNum, 2 )) + "/(!" + Str(initialValueDen) + "+" + Str(initialValueDen) + ")"
Else
result = result + Str(Math.Round(initialValueNum, 2 )) + "/(!" + Str(initialValueDen) + "+" + Str(initialValueDen) + ") + "
End If
End If
initialValueNum -= (t / 100 )
initialValueDen += 1
Next
Return "F = " + result
End Function # Output: RegularSerieWithFactorial(TextBox1.Text, vi, r, True)
F = 4.750333333333333
# Output string: RegularSerieWithFactorial(TextBox1.Text, vi, r, False)
F = 5.25/( ! 0+0) + 5.24/( ! 1+1) + 5.22/( ! 2+2) + 5.19/( ! 3+3) + 5.15/( ! 4+4) + 5.1/( ! 5+5)
F = X^2/2! + X^4/4! + X^6/6!+… X，只是一个输入变量，必须在术语中取
Public Function SumFactorial(n As Integer , x As Single , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim formule As Double
If n = 0 Then
result = Str( 0 )
End If
For index = 1 To n
If sumTotal Then
formule = Math.Pow(x, index * 2 ) / Factorial(index * 2 )
result = Str(formule)
Else
If index = n Then
result = result + "(" + Str(x) + "^" + Str(index * 2 ) + ")/" + Str(index * 2 ) + "!"
Else
result = result + "(" + Str(x) + "^" + Str(index * 2 ) + ")/" + Str(index * 2 ) + "! + "
End If
End If
Next
Return "F = " + result
End Function # Output: SumFactorial(TextBox1.Text, TextBox2.Text, True)
F = 0.0002821869488536155
# Output string: SumFactorial(TextBox1.Text, TextBox2.Text, False)
F = (2^2)/ 2 ! + (2^4)/ 4 ! + (2^6)/ 6 ! + (2^8)/ 8 ! + (2^10)/ 10 ! 
3√(0+x1) + 6√(1+x1) + 9√(1+x1)...根参数是斐波那契加上变量 x1。
Public Function SerieProgresiveFibonacci(n As Integer , x As Double , viRoot As Integer , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index, a, b, c, root As Integer
Dim formule, total As Double
a = - 1 : b = 1 : root = viRoot
For index = 1 To n
c = a + b
If sumTotal Then
formule = (c + x) ^ ( 1 / root)
total += formule
result = Str(total)
Else
If index = n Then
result = result + Str(index * 3 ) + "√(" + Str(c) + "+" + Str(x) + ")"
Else
result = result + Str(index * 3 ) + "√(" + Str(c) + "+" + Str(x) + ") + "
End If
End If
a = b
b = c
root *= 3
Next
Return "F = " + result
End Function # Output: SerieProgresiveFibonacci(TextBox1.Text, TextBox2.Text, TextBox3.Text, True)
F = 5.455187736786854
# Output string: SerieProgresiveFibonacci(TextBox1.Text, TextBox2.Text, TextBox3.Text, False)
F = 3√(0+2) + 6√(1+2) + 9√(1+2) + 12√(2+2) + 15√(3+2)
20√cos(0.2) - 19√cos(0.4) + 18√cos(0.6)... “pimponea”，即项加减，加减。这不是 N 项，但直到根为 2，所以最后一个元素将为 2√cos(...)。
Public Shared Function Pinponear(root As Double , vi As Double , razon As Double , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim count, total, formule As Double
count = vi
For index = root To 2 Step - 1
If sumTotal Then
If index Mod 2 <> 0 Then
formule = -Math.Pow(Math.Cos(count), 1 / index)
Else
formule = Math.Pow(Math.Cos(count), 1 / index)
End If
total += formule
result = Str(total)
Else
If index = 2 Then
result = result + Str(index) + "√cos(" + Str(count) + ")"
Else
If index Mod 2 <> 0 Then
result = result + Str(index) + "√cos(" + Str(count) + ") + "
Else
result = result + Str(index) + "√cos(" + Str(count) + ") - "
End If
End If
End If
count = Math.Round(count + razon, 2 )
Next
Return "F = " + result
End Function # Output: Pinponear(TextBox1.Text, vi, r, True)
F = 5.455187736786854
# Output string: Pinponear(TextBox1.Text, vi, r, False)
F = 3√(0+2) + 6√(1+2) + 9√(1+2) + 12√(2+2) + 15√(3+2)
√(sin(0.1)/(3!/2)) + √(sin(0.11)/(3!/2))...它还会 ping、减法和加法、减法和加法。
Public Function ProgresiveSeriePinponear(n As Integer , initValue As Double , r As Double , arg As Double , sumTotal As Boolean )
Dim result As String = ""
Dim index As Integer
Dim total, formule, count As Double
count = initValue
For index = 1 To n
If sumTotal Then
formule = Math.Sqrt(Math.Sin(arg) / (Factorial(count) / 2 ))
total = -total + formule
result = Str(total)
Else
If index Mod 2 = 0 Then
result = result + "+ √sin(" + Str(arg) + ")/(" + Str(count) + "!/2) "
Else
result = result + "- √sin(" + Str(arg) + ")/(" + Str(count) + "!/2) "
End If
End If
arg = Math.Round(arg + r, 2 )
count += 3
Next
Return "F = " + result
End Function # Output: ProgresiveSeriePinponear(TextBox1.Text, vi, r, arg, True)
F = -0.16574853902978934
# Output string: ProgresiveSeriePinponear(TextBox1.Text, vi, r, arg, False)
F = - √sin( 0.1)/( 3 ! /2) + √sin( 0.11)/( 6 ! /2) - √sin( 0.12)/( 9 ! /2) + √sin( 0.13)/( 12 ! /2)
(π/2)/√(1000+0) + (π/1.9)/√(1001+1) + (π/1.8)/√(1003+1)根的幅角逐级增加：从第 1 次开始至第 2 个 1；从第 2 次到第 3 次 2；从第3个到第4个3； …而另一个是斐波那契。
Public Function ProgresiveSerieFibonacci(n As Integer , initValue As Integer , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim count, a, b, c, total, formule As Double
count = 2 : a = - 1 : b = 1
For index = 1 To n
c = a + b
If sumTotal Then
formule = ( 3.14159 / count) / Math.Sqrt(initValue + c)
total += formule
result = Str(total)
Else
If index = n Then
result = result + "(π/" + Str(count) + ")/√(" + Str(initValue) + "+" + Str(c) + ")"
Else
result = result + "(π/" + Str(count) + ")/√(" + Str(initValue) + "+" + Str(c) + ") + "
End If
End If
a = b
b = c
count = Math.Round(count - 0.1 , 2 )
initValue += index
Next
Return "F = " + result
End Function # Output: ProgresiveSerieFibonacci(TextBox1.Text, TextBox2.Text, True)
F = 0.27688777750129406
# Output string: ProgresiveSerieFibonacci(TextBox1.Text, TextBox2.Text, False)
F = (π/ 2)/√( 1000+ 0) + (π/ 1.9)/√( 1001+ 1) + (π/ 1.8)/√( 1003+ 1) + (π/ 1.7)/√( 1006+ 2) + (π/ 1.6)/√( 1010+ 3)
2√x^2/100 + 4√x^4/50 + 8√x^8/25...根相乘，而根内的分母展开（除）。
Public Function SerieMultiplyAndUnfold(n As Integer , root As Double , num As Double , denom As Double , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim total, formule As Double
For index = 1 To n
If sumTotal Then
formule = Math.Pow(Math.Pow(num, root) / denom, 1 / root)
total += formule
result = Str(total)
Else
If index = n Then
result = result + Str(root) + "√(" + Str(num) + "^" + Str(root) + "/" + Str(denom) + ")"
Else
result = result + Str(root) + "√(" + Str(num) + "^" + Str(root) + "/" + Str(denom) + ") + "
End If
End If
root = Math.Round(root * 2 , 2 )
denom = Math.Round(denom / 2 , 2 )
Next
Return "F = " + result
End Function # Output: SerieMultiplyAndUnfold(TextBox1.Text, TextBox2.Text,TextBox3.Text, TextBox4.Text, True)
F = 1.9987716171427177
# Output string with params: SerieMultiplyAndUnfold(4, 2, 1, 100, False)
F = 2√( 1^ 2/ 100) + 4√( 1^ 4/ 50) + 8√( 1^ 8/ 25) + 16√( 1^ 16/ 12.5)
( 2+x^(1/16)) + (4+x^(1/14))...基数加倍。小心，直到 X 上升到 1/2 为止
Public Function SerieBaseIsDoubling(n As Integer , base As Double , x As Double , denom As Double , sumTotal As Boolean ) As String
Dim result As String = ""
Dim index As Integer
Dim total, formule As Double
For index = 1 To n
If sumTotal Then
formule = base + Math.Pow(x, 1 / denom)
total += formule
result = total
Else
If denom >= 2 Then
If index = n Then
result = result + "(" + Str(base) + "+" + Str(x) + "^(1/" + Str(denom) + "))"
Else
result = result + "(" + Str(base) + "+" + Str(x) + "^(1/" + Str(denom) + ")) + "
End If
End If
End If
base *= 2
denom -= 2
Next
Return "F = " + result
End Function # Output: SerieBaseIsDoubling(TextBox1.Text, vi, r, arg, True)
F = 2056
# Output string with params: SerieBaseIsDoubling(10, 2, 1, 16, False)
F = ( 2+ 1^(1/ 16)) + ( 4+ 1^(1/ 14)) + ( 8+ 1^(1/ 12)) + ( 16+ 1^(1/ 10)) + ( 32+ 1^(1/ 8)) + ( 64+ 1^(1/ 6)) + ( 128+ 1^(1/ 4)) + ( 256+ 1^(1/ 2))
