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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,……….then |
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Answer» `T_(n)gt167/60` `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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