If n is a positive integer, for `(1+x)^(n)` ,then `sum_(r=0)^(n).^nC_(r)=`

Assertion: If n is an even positive integer n then sum_(r=0)^n ^nC_r/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ^nC_r/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: If n is an even positive integer n then sum_(r=1)^(n-1)1/(|__r|__n-r)=2^(n-1)/(|__n) . Reason: ^nC_1+^nC_3+……..+^nC_(n-1)=2^(n-1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

prove that sum_(r=0)^(n)3^(r)nC_(r)=4^(n)

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

If n is a positive integer,sum_(r=0)^(n)(^(^^)nC_(r))^(2)=

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

Find sum_(r=0)^n(r+1)*"^nC_rx^r

If n is a positive integer,then nC_(1)+nC_(2)+...+nC_(n)=2^(n)-1

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

If n is a positive integer and if (1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r) , then