Prove that`sum_(r=1)^k(-3)^(r-1)C(3n,2r-1)=0`, where `k=(3n)/2` and `n` is an even positive integer.

Prove that sum_(r=1)^(k)(-3)^(r-1)3nC_(2r-1)=0, where k=(3n/2 and n is an even integer

Prove that sum_(r=1)^(k)(-3)^(r-1)3nC_(2r-1)=0, where k=3n/2 and n is an even integer.

Prove that sum_(k=1)^(n-1)(n-k)(cos(2k pi))/(n)=-(n)/(2) wheren >=3 is an integer

If sum_(r=1)^(n)r^(3)((C(n,r))/(C(n,r-1)))=14^(2) then n=

Prove that sum_(r=0)^(s)sum_(s=1)^(n)C_(s)^(n)C_(r)=3^(n)-1

If C_(r) stands for ""^(n)C_(r) , then the sum of the series (2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-...+(-1)^(n)(n+1)C_(n)^(2)] , where n is an even positive integers, is:

If C_(r) stands for nC_(r), then the sum of the series (2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-......+(-1)^(n)(n+1)C_(n)^(2)], where n is an even positive integer,is

The sum of the series sum_(r=0)^(n)(-1)^(r)(n+2r)^(2) (where n is even) is equal to

If n is a positive integer,then sum_(r=2)^(n)r(r-1)*C_(r) =