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)+…

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

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

If m=""^(n)C_(2) , then ""^(m)C_(2) is equal to a) 3""^(n)C_(4) b) ""^(n+1)C_(4) c) 3""^(n+1)C_(4) d) 3""^(n+1)C_(3)

If n=5 , then (""^(n)C_(0))^(2)+(""^(n)C_(1))^(2)+(""^(n)C_(2))^(2)+......+(""^(n)C_(5))^(2) is equal to a)250 b)254 c)245 d)252

If ""^(n)C_(2) + ""^(n)C_(3) = ""^(6)C_(3) and ""^(n)C_(x) = ""^(n)C_(3), x != 3 , then the value of x is

Find the sum of the series ""^(15)C_(0)+^(15)C_(1)+^(15)C_(2)+….+^(15)C_(7) .

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