Prove that `sum_(r=1)^k(-3)^(r-1)^(3n)C_(2r-1)=0,w h e r ek=3n//2` and`n` is an even integer.

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

sum_(r=1)^k(−3)^(r−1) .^(3n)C_(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_(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) ""^(3n)C_(2r-1) = 0 , where k = 3n//2 and n is an even integer.

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 underset(r=1)overset(k)sum(-3)^(r-1) .^(3n)C_(2r-1) = 0 , where k = (3n)/2 and n is an even integer.

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

Prove that sum_(k=1)^(n-r ) ""^(n-k)C_(r )= ""^(n)C_( r+1) .