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)

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

Find the sum sum_(k=0)^n ("^nC_k)/(k+1)

prove that sum_(k=1)^(n)k2^(-k)=2[1-2^(-n)-n*2^(-(n+1)))

Prove that sum_(k=1)^(n-1) ""^(n)C_(k)[cos k x. cos (n+k)x+sin(n-k)x.sin(2n-k)x]=(2^(n)-2)cos nx .