int_(0)^(1)(prod_(r=1)^(n)(x+r))(sum_(k=1)^(n)(1)/((x+k)))dx=

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 ( 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:

If lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(r)))/(sum_(r=1)^(n)r)=(k)/(3) then the value of k is

Let f(n)=(sum_(r=1)^(n)((1)/(r)))/(sum_(k=1)^(n)(k)/(2n-2k+1)(2n-k+1))

If I_(1)=int_(0)^(1)prod_(r=1)^(2016)(r-x)dx and I_(2)=int_(0)^(1)prod_(r=0)^(2015)(r+x)dx, then (I_(1))/(I_(2)) is equal to 2(b)(1)/(2)(c)-1 (d) 1

If sum_(r=1)^(n)t_(r)=sum_(k=1)^(n)sum_(j=1)^(k)sum_(i=1)^(j)2, then sum_(r=1)^(n)(1)/(t_(r))=

(1+x)(sum_(r=0)^(n)nC_(r)x^(r))+(1+x^(2))(sum_(r=0)^(n-1)(n-1)C_(r)x^(r))+...(1+x^(n))(sum_(r=0)^(1)1C_(r)x^(r))=a_(0)+a_(1)x+, then the value of (a_(1))/(a_(n)+1)+(a_(1))/(a_(n))+(a_(2))/(a_(n-1))+......+(a_(n+1))/(a_(0)) is equal to

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

If int _(0)^(1) (sum _(r=1) ^(2013)(x)/(x ^(2)+r ^(2)) prod_(r=1)^(2013)(x ^(2) +r ^(2) )) dx =1/2 [(prod_(r=1)^(2013)(1+r ^(2)))-k^(2)] then k=