If `sum_(r=0)^nr/(^n C_r)=sum_(r=0)^n(n^2-3n+3)/(2.^n C_r)` , then a.`n=1` b. `n=2` c. `n=3` d. none of these

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

If sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64) where n, p in N , then

Find the sum of sum_(r=1)^n(r^n C_r)/(n C_(r-1) .

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

If s_(n) = sum_(r = 0)^(n) 1/(""^(n)C_(r)) and t_(n) = sum _(r = 0)^(n) r/(""^(n)C_(r)) ,then t_(n)/s_(n) is equal to

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is

Find the sum sum_(r=0)^n^(n+r)C_r .

Prove that (3!)/(2(n+3))=sum_(r=0)^n(-1)^r((^n C_r)/(^(r+3)C_r))

Prove that sum_(r=0)^(2n)r(.^(2n)C_r)^2=n^(4n)C_(2n) .