Final answer:
To find out how many terms of the alternating series you need to add for a specific accuracy, you can use the Alternative Series Estimation Theorem.
Step-by-step explanation:
To determine how many terms of the alternating series you need to add so that the partial sum and the infinite sum differ by less than 0.00005, you can use the Alternative Series Estimation Theorem. This theorem states that if the terms in an alternating series are decreasing in absolute value and approach zero, then the difference between the partial sum and the infinite sum is less than or equal to the absolute value of the first omitted term.
In this case, you want the difference to be less than 0.00005. So, you need to find the smallest value of n such that the absolute value of the (n+1)th term is less than 0.00005. You can solve this equation to find the value of n:
|an+1| < 0.00005
Once you find the value of n, you add the first n terms of the series to get an approximation of the infinite sum within the desired accuracy.