If `sum_(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e ,` then a. `a-b=d-c` b.`e=0` c.`a , b-2//3,c-1` are in A.P. d.`c/a` is an integer

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

If ^n+1C_(r+1) : ^n C_r : ^(n-1)C_(r-1)=11 :6:3, then n r =

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

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

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

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

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

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.

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

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