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1. ## calculating series

The question I am having problems with is the following:

Write a method to compute the following series:

m(i) = 4(1 - 1/3 + 1/5 -1/7 + 1/9 - 1/11 + ... + 1/(2i-1) - 1/(2i+1)

here is the code I have put together so far:

Code:
```public class series {

public static double m(int i){

double num = 0;

for (i = i;i>0;i--){ //infinite times starting at i
num += 4*((1/(2*((double)i)-1))-(1/(2*((double)i)+1)));
}
return num;
}
public static void main(String args[]){
System.out.println("i     m(i)");
for (int i=10;i<=100;i=i+10)
System.out.println(i+"     "+(m(i)));
}
}```
for some reason it is not displaying the correct results what am I missing?

The expected print out is :

i m(i)
10 3.04184
20 3.09162

etc but mine is starting at 3.809

• Is the formula correct?

With your logic in code I a1ways get this:
i=10; num = 4(1/19 -1/21)
i=9; num=4(1/17-1/19)
i=8; num=4(1/15-1/17)
i=7; num=4(1/13-1/15)
i=6; num=4(1/11-1/13)
i=5; num=4(1/9-1/11)
i=4; num=4(1/7-1/9)
i=3; num=4(1/5-1/7)
i=2; num=4(1/3-1/5)
i=1; num=4(1-1/3)

Total will be 3.80952380952381

And with m(i) formula you gave above with m= 10, I always get m(10) = 1-1/3+1/5-1/7+1/9-1/11+1/13-1/15+1/17-1/19+1/21

it is not matched to 1/(2i-1) + 1/(2i+1). Please revise the formula once..

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