`sum_(k=0)^20(.^20C_k)^2 = ?`

sum_(k=0)^(20)(.^(20)C_(k))^(2) is equal to

Find the sum sum_(k=0)^(10)2^(20)C_(k)

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 ............

sum_(i=1)^20 (.^20C_(i-1))/(.^20C_i+.^20C_(i-1))=k/21 then find the value of k. (a) 400 (b) 100 (c) 50 (d) 200

If f(x)-f(y)=In(x/y)+x-y then find sum_(k=1)^20f'(1/k^2)

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

The coefficient of x^(50) in the expansion sum_(k=0)^(100)""^(100)C_(k)( x-2)^(100-k)3^(k) is also equal to :