come up with an alternating series that satisfies the first two conditions of th

Question

come up with an alternating series that satisfies the first two conditions of the alternating series test for convergence, but not the third. a equation: the sum of (-1)^n+1 b_n, n=1 to infinity ; with b_n >0, b_n -> 0 as n -> infinity, but the sequence b_n eventually doesn't decrease.

Explanation / Answer

there are two condition for sequence a_n to be convergent in alternating series test: 1) lim n--->infinity b_n = 0.. 2) b_n is decreasing sequence. hence a possible alernating series may be: summation of ((-1)^(n+1))/n from n =1 to n = infinity, first test for this lim n--->infinity b_n = 0, so here b_n is 1/n put n ifinity it will become zero, second condition is also satisfied as b_n is decreasing series

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