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Let `S_(n)=sum_(r=1)^(n)((r^(4)_r^(3)n+r^(2)n^(2)+2n^(4))/(n^(5)))` and `T_(n)=sum_(r=0)^(n-1)((r^(4)+r^(3)n^(2)+2n^(4))/(n^(5))),n=1,2,3,`……….thenA. `T_(n)gt167/60`B. `T_(n)lt167/60`C. `S_(n)gt167/60`D. `S_(n)lt167/60` |
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Answer» Correct Answer - B::C `T_(n)=1/n sum_(r=0)^(n-1) (r/n)` where `f(x)=x^(4)+x^(3)+x^(2)+2, f(x)` is an increasing function for `AA x gt 0`. `T_(n)=1/n[f(0)+f(1/n)…+f((n-1)/n)]` `T_(n)lt int_(0)^(1)(x^(4)+x^(3)+x^(2)+2)dx=167/60` `S_(n)=1/n sum_(r=1)^(n)(f (r/n)gt 1/n[f(1/n)+...+f(r/n)]=167/60` |
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