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

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

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

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

Let f(n)=sum_(k=-n)^(n)(cot^(-1)((1)/(k))-tan^(-1)(k)) such that sum_(n=2)^(10)(f(n)+f(n-1))=a pi then find the value of (a+1) .

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2

S_(n)=sum_(k=1)^(n)(k^(2)+n^(2))/(n^(3)) and T_(n)=sum_(k=0)^(n-1)(k^(2)+n^(2))/(n^(3)),n in N then

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

If n in N and sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2)=(n(n+1)^(2)(n+2))/(3p) then the value of p is