If `1+n+n^(2)+...+n^(127)=(1+n+n^(2)+...+n^(63))(n^(k)+1)` ,then the value of k 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

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

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 n is a positive integer and (1+i)^(2n)=k cos(n pi/2) , then the value of k is

lim_(nrarroo)(1/(n+1)+1/(n+2)+…….+1/(6n))=kln6 , then find the value of k

lim_(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."+n^(2))(1^(3)+2^(3)+"....."+n^(3))) = F(k) , then (k in N)