Tuesday, 28 April 2015

calculus - Find limlimitsntoinftysumlimitsnk=1frac2k+1k2(k+1)2




I have to find the limit limnnk=12k+1k2(k+1)2.

I tried to make it into a telescopic series but it doesn't really work out...



limnnk=12k+1k2(k+1)2=nk=1(1kk2+1k+11(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



limnnk=1[1k21(k+1)2]



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