The value of `int_0^1 ( pi_(r=1)^n (x+r)) (sum_(k=1)^n 1/(x+k)) dx`

Find sum_(k=1)^(n)(1)/(k(k+1)) .

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of int_0^pi (sin(1+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

Evaluate : int_(0)^(1)x(1-x)^(n)dx .

Find the value of lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

The value of lim_(n->oo)sum_(r=0)^(n) (sum_(t=0)^(r-1)1/(5^n)*"^n C_r * "^r C_t .(3^t)) is equal to

Evaluate int_(0)^(1)x(1-x)^(n)dx

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .