Is there a method to prove the sequence an= 1/(n+1) + 1/(n+2)+...+1/2n is convergent, or the only way to explain it is that it's obvious that the sequence will approach 0 as the n increases but it will never get to 0. So it's monotonically decreasing and is limited by 0 beneath it, so it's convergent! I tried using the squeeze theorem, but I get n/n+1>an>n/2n, and n/n+1 is limited by 1, and n/2n is limited by 1/2, so it doesn't prove whether an is convergent. Someone please help!
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It doesn't converge to $0,$ it converges to $\ln 2.$ But this is a duplicate question. – Adam Rubinson Jan 30 '24 at 10:37