Let `k=1^@`, then prove that `sum_(n=0)^88 1/(cosnk* cos(n+1)k)=cosk/sin^2k`

Let k=1^(@) then prove that sum_(n=0)^(88)(1)/(cos nk cos(n+1)k)=(cos k)/(sin^(2)k)

Prove that sum_(k=1)^n 1/(k(k+1))=1−1/(n+1) .

If a_k=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum_(k=1)^n a_k)^2 =n^2/(n+1)^2

Prove that sum_(k=1)^(n)(1)/(k(k+1))=1-(1)/(n+1).

Prove that sum_ (k = 0) ^ (n) nC_ (k) sin Kx.cos (nK) x = 2 ^ (n-1) sin nx

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

Let S_k=1+q+q^2+...+q^k and T_k=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^k q!=1 then prove that sum_(r=1)^(n+1) ^(n+1)C_rS_(r-1)=2^ nT_n

Prove that Sigma_(K=0)^(n) ""^nC_(k) sin K x cos (n-K)x = 2^(n-1) sin x.

Prove that : sum_(i=0)^r((n+i),(k))=((n+r+1),(k+1))-((n),(k+1))