Infinite Series

Intermediate Exercise

Statement

Create a Function where the user enters $n$ numbers of terms desired for a series and is returned its sum, the series being the following: $$S={1 \over 1^3} - {1 \over 3^3} + {1 \over 5^3} - {1 \over 7^3}+...$$

Suggested Concepts:

Dim
For Next
Function

Remember that in most cases there is more than one way to solve the exercise.

Hint: Create a Loop with a given "$n$" and try to realize the pattern that exists in the series to be replicated.

Solved Exercise

Exercise Solution

We start by defining the arguments of the series and the output data type
```
Function InFSeR(n As Double) As Double
```
We define the variables
```
Dim i As Double
Dim Prog As Double
```
We create a For Next loop from 1 to $n$. The "Prog" variable was created to allow us to progress in the sum until we reach the n^th term
```
For i = 1 To n
    Prog = Prog + (-1) * ((-1) ^ i) * (1 / ((2 * i - 1) ^ 3))
Next i
```
We define the output of the Function as the variable Prog when the For Next loop is done
```
InFSeR = Prog
```

Consolidated Answer

Function InFSeR(n As Double) As Double

    Dim i As Double
    Dim Prog As Double

    For i = 1 To n

        Prog = Prog + (-1) * ((-1) ^ i) * (1 / ((2 * i - 1) ^ 3))

    Next i

    InFSeR = Prog

End Function

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