I have to find the limit limn→∞n∑k=12k+1k2(k+1)2.
I tried to make it into a telescopic series but it doesn't really work out...
limn→∞n∑k=12k+1k2(k+1)2=n∑k=1(1−kk2+1k+1−1(k+1)2)
so that is what I did using telescopic...
I said that:
2k+1k2(k+1)2=Ak+Bk2+Ck+1+D(k+1)2
but now as I look at it.. I guess I should "build up the power" with the k2 too, right?
Answer
limn→∞n∑k=1[1k2−1(k+1)2]
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