Find the sum `C_(0)-C_(2) +C_(4)-C_(6)+….`, where `C_(r)=^(n)C_(r)`

Find the sum ""^(n)C_(0)+""^(n)C_(4)+^(n)C_(8)....

Find the sum 3^(n)C_(0)-8^(n)C_(1)+13^(n)C_(2)-18 xx ^(n)C_(3)+…

Find the sum ""^(10)C_(1) +^(10)C_(3) +^(10)C_(5)+^(10)C_(7)+^(10)C_(9) .

Prove that (C_(1))/(2)+(C_(3))/(4) +(C_(5))/(6)+….=2^(n)/(n+1) where C_(r) =^(n)C_(r)

The arithmetic mean of ""^(n)C_(0), ""^(n)C_(1), ""^(n)C_(2)…., ""^(n)C_(n) is

Find the sum overset(n)underset(r=1) Sigma (r""^(n)C_(r))/(""^(n)C_(r-1))

If (1+x)^(15)=C_(0)+C_(1)x+C_(2)x^(2)+....+C_(15^(x^(15))) , then find the sum of 2 C_(2)+2.3 C_(3)+3.4 C_(4)+….+14.15 C_(15)

Prove that ""^(n)C_(0)""^(n)C_(0)-^(n+1)C_(1) ""^(n)C_(1)+^(n+2)C_(2)""^(n)C_(2)....=(-1)^(n)