" If "sum_(n=1)^(5)(1)/(n(n+1)(n+2)(n+3))=(k)/(3)," then "k" is equal to "

sum_(n=1)^oo 1/((n+1)(n+2)(n+3).........(n+k))

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

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_(r=0)^n(2r+3)/(r+1), C_r=((n+k)*2^(n+1)-1)/(n+1) then 'k' is

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) is equal to

Prove that sum_(k=1)^(n-1)(n-k)(cos(2k pi))/(n)=-(n)/(2) wheren >=3 is an integer

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