Finding Sum of Alternating Series to Desired Accuracy

[lindsaygilber]

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

The alternating series from n=1 to infinity of ((-1)^(n+1))/(n^2)
|error| less than 0.0399
i got it down to 1/n^2 is less than 0.0399 but i can't figure out if n = 5 or n=6... please help:(

 

[HallsofIvy]

If you want 1/n²< 0.0399, then you want 1/0.0399= 25.0626< n² While it is close hat is NOT true for n= 5.