If`(1^2-t_1)+(2^2-t_2)+….+(n^2-t_n)=(n(n^2-1))/(3)` then `t_n` is equal to

If s_(n) = sum_(r = 0)^(n) 1/(""^(n)C_(r)) and t_(n) = sum _(r = 0)^(n) r/(""^(n)C_(r)) ,then t_(n)/s_(n) is equal to

The value of sum sum_(n=1)^(oo)cot^(-1)(((n^(2)+2n)(n^(2)+2n+1)+1)/(2n+2)) is equal to

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

lim_(ntoinfty) (n/(n^2+1^2)+n/(n^2+2^2)+n/(n^2+3^2)+...+1/(2n)) is equal to

(n+2)nC_0(2^(n+1))-(n+1)nC_1(2^(n))+(n)nC_2(2^(n-1))-.... is equal to

lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)] is equal to

lim_(n rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is equal to

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to

The absolute value of the sum of first 20 terms of series, if S_(n)=(n+1)/(2) and (T_(n-1))/(T_(n))=(1)/(n^(2))-1 , where n is odd, given S_(n) and T_(n) denotes sum of first n terms and n^(th) terms of the series