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

The value of int_(0)^(1)lim_(n rarr oo)sum_(k=0)^(n)(x^(k+2)2^(k))/(k!)dx is:

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

The value of integral sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx is

The value of sum_(n=1)^100 int_(n-1)^n e^(x-[x])dx =

The value of sum_(r=1)^(n+1)(sum_(k=1)^(k)C_(r-1))( where r,k,n in N) is equal to a.2^(n+1)-2b2^(n+1)-1c.2^(n+1)d. none of these

The value of lim_(x rarr0)[(1-2x)^(n)sum_(r=0)^(n)-r((x+x^(2))/(1-2x))^(r)]^((1)/(x)) is :

The value of sum_(n=0)^(1)sum_(i=1r<=pi)^( n)nC_(r)sC_(r) is