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Consider a function f(n)=1/(1+n)^2. Let ...

Consider a function `f(n)=1/(1+n)^2.` Let `alpha_n=1/n sum_(r=1)^n f(r/n) and beta_n=1/n sum_(r=0)^(n-1) f(r/n)` for `n=1,2,3,.....` Also `alpha = lim_(n ->oo) alpha _n & beta = lim_(n->oo) beta_n.` Then prove

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