Is this a good example of an alternating series whose terms

Solution

here if we will write the summation form of series, we will get summation from n = 1 to infinity (-1)^(n)(1/n) where bn = 1/n now for convergence we know that for any alternating series 1. bn must be decreasing and 2. limit n tends to infinity bn = 0 here we can see in the given series is decreasing. now, we need to check whether the limiting value is = 0 or not so, limit n tends to infinity (1/n) as we know that 1/infinity = 0 so, we will get the limit value is = 0 that means it fulfills the criteria for convergence!! So, result is convergence for this given series. Hope this will help you!!