Final answer:
Without the specific formula for the alternating series, it is not possible to determine how many terms are needed to ensure that the partial sum and infinite sum differ by less than 0.00005.
Step-by-step explanation:
To determine how many terms of an alternating series are required to ensure that the partial sum differs from the infinite sum by less than 0.00005, we need to know more about the specific series in question.
Typically, you would use the remainder estimate for the alternating series test, which states that the absolute value of the remainder Rn (the difference between the partial sum Sn and the infinite sum S) when n terms are used is less than or equal to the absolute value of the (n+1)th term.
Without the explicit series or a general term given, we cannot proceed to calculate the exact number of terms required.
The provided information does not contain a clear sequence formula for the alternating series in question, thus, it is not possible to confidently provide an answer regarding the number of terms needed.
Remember, the key in evaluating alternating series for convergence and estimating sums to a certain precision lies in understanding the behavior of the series' terms and applying the correct convergence tests.