`sum_(k=m)^n kC_r`

The value of sum_(r=1)^(n+1)(sum_(k=1)^n ^kC_(r-1)) (where r, k, n in N ) is equal to

Let f(n)=sum_(r=0)^nsum_(k=r)^n(kC r) Find the total number of divisors of f(9)dot

Prove that ""^(n+1)C_2+2*sum_(k=2)^n""^kC_2=sum_(k=1)^nk^2

If (1+x)^n=sum_(r=0)^n .^nC_r x^r then sum_(r=m)^n .^rC_m is equal to

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^(k)C_(r-1))( where r,k,n in N) is equal to a.2^(n+1)-2b2^(n+1)-1c.2^(n+1)d. none of these

Show that sum_(k =0)^(n) C_(k) *sin (kx) cos (n-k) x = 2^(n-1)sin n x where C_(r )= ""^(n)C_(r )

""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :