If `n in N` and `sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2)=(n(n+1)^(2)(n+2))/(3p)` then the value of `p` is

If C_(r) = ""^(n)C_(r) and (C_(0) + C_(1)) (C_(1) + C_(2)) … (C_(n-1) + C_(n)) = k ((n +1)^(n))/(n!) , then the value of k, is

sum_(k=1)^(oo)k(1-(1)/(n))^(k-1)=a*n(n-1)bn(n+1)c*n^(2)d.(n+1)^(2)

sum_ (k = 1) ^ (n) (2 ^ (k) + 3 ^ (k-1))

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value

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

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