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 sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to

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

The value of lim_(n rarroo) sum_(r=1)^(n)(1)/(sin{((n+r)pi)/(4n)}).(pi)/(n) is equal to

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

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

The value of sum_(n=1)^(oo)(""^(n)C_(0)+.......+""^(n)C_(n))/(""^(n)P_(n))

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

Let f(x)=lim_(nrarroo) sum_(r=0)^(n-1)(x)/((rx+1){(r+1)x+1}) . Then