Given (a_n = frac{(-1)^n}{sqrt{n+1}}), consider the series (sum_{n=1}^{infty} a_n). Find the set of real numbers (x) for which the series converges. Write your answer in interval notation. Interval for convergence: (x in (-1, 1])
Added by Timothy R.
Step 1
The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series converges. In this case, the terms of the series \(\sum_{n=1}^{\infty} a_n\) alternate in sign (\((-1)^n\)) and decrease in Show more…
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