The value of `sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1)` is equal to a.`-1/(n+1)` b. `1/n` c. `1/(n+1)` d. `n/(n+1)`

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is

The value of sum_(r=0)^(3n-1)(-1)^r 6nC_(2r+1)3^r is

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

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-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 lim_(n rarroo) sum_(r=1)^(n)(1)/(sin{((n+r)pi)/(4n)}).(pi)/(n) is equal to

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

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

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

The value of ("lim")_(nvecoo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to 1/(35) (b) 1/4 (c) 1/(10) (d) 1/5