sum_(n=1)^infty ((-1)^n-1(2 n+1))/(n(n+1))=1 old góster

The given series is . We need to determine if this series converges to 1.To do this, we can use the Alternating Series Test. The Alternating Series Test states that if the terms of an alternating series decrease monotonically and approach zero, then the series converges.Let's apply the Alternating Series Test to our series:1. The terms of the series are alternating in sign, since we have .2. The terms of the series are decreasing monotonically, since is increasing.3. The terms of the series approach zero as approaches infinity.Since all three conditions of the Alternating Series Test are satisfied, we can conclude that the series converges.To find the sum of the series, we can use the formula for the sum of an alternating series: Therefore, the correct answer is 1.