Monday, 14 March 2016

calculus - Bounding a series: fracpi2<sumin=0nftyfrac1n2+1<frac3pi2

I have the following statement -




π2<n=01n2+1<3π2



So I tried to prove this statement using the integral test and successfully proved the lower bound. But when I tried to calculate the upper bound I was required to calculate the integral from -1 - 11x2+1dx.
If someone can explain why it will be great , thanks!

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