Value of `sum_(k=1)^oosum_(r=0)^k1/(3^k)(^k C_r)` is `2/3` b. `4/3` c. `2` d. `1`

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

Find the value off sum_(k1)^10(2+3^k)

sum_(k=1)^(oo)sum_(r=1)^(k)1/(4^(k))(""^(k)C_(r)) is equal to=________

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Sum of the series sum_(k=1)^(oo)sum_(r=0)^(k)(2^(2r))/(7^(k))(""^(k)C_(r)) is:

sum_ (k = 1) ^ (n) (2 ^ (k) + 3 ^ (k-1))

Evaluate the sum , sum_(k=1)^(n)(1)/(k(k+1)(k+2)……..(k+r)) .

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

If sum_(k=1)^n(sum_(m=1)^k m^2)=a n^4+b n^3+c n^2+dn+e then -