Prove that `sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2,w h e r engeq3i sa nin t ege r`

Similar Questions

Explore conceptually related problems

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

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

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

Prove that sum_(r=1)^k(-3)^(r-1)^(3n)C_(2r-1)=0,w h e r ek=3n//2 and n is an even integer.

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

Prove that sum_(r=0)^(2n)r(.^(2n)C_r)^2=n^(4n)C_(2n) .

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

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

Evaluate: ("lim")_(n->oo)(-1)^(n-1)sin(pisqrt(n^2+0. 5 n+1)),w h e r en in N