Find the sum of the series `sum_(r=1)^(n) r x^(r-1)` using calculus .

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

Evaluate sum_(r=1)^(n)rxxr!

The coefficient of x^(50) in the series sum_(r=1)^(101)rx^(r-1)(1+x)^(101-r) is

Find the sum sum_(r=0)^n^(n+r)C_r .

Find he value of sum_(r=1)^(4n+7)\ i^r where, i=sqrt(- 1).

If A_(1), A_(3), ... , A_(2n-1) are n skew-symmetric matrices of same order, then B =sum_(r=1)^(n) (2r-1) (A_(2r-1))^(2r-1) will be

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) where T_(r) denotes the rth term of the series. Find lim_(nto oo) sum_(r=1)^(n)(1)/(T_(r)) .

Find the value of sum_(r=1)^(10)sum_(s=1)^(10)tan^(-1)(r/s)dot

The sum sum_(r=0)^n (r+1) (C_r)^2 is equal to :