माना कि किसी धनात्मक पूर्णांक n के लिए det [(sum_(k=0)^(n)k,sum_(k=0)^(n).^(n)C_(k)k^(2)),(sum_(...

sum_(k=1)^n k^3=

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

Suppose det [{:(sum_(k=0)^(n)k,,sum_(k=0)^(n).^nC_(k)k^2),(sum_(k=0)^(n).^nC_(k)k,,sum_(k=0)^(n).^nC_(k)3^(k)):}]=0 holds for some positive integer n. then sum_(k=0)^(n)(.^nC_(k))/(k+1) equals ............

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

If sum_(k=1)^(n)k=210, find the value of sum_(k=1)^(n)k^(2).

If sum_(k=1)^(n)k=45, find the value of sum_(k=1)^(n)k^(3).