Let `S(n)=sum_(r=1)^n(cos(2*3^(r-1)alpha)/(sin(3^ralpha),alpha=1 8^(@)) and P(n) =sum_(r=1)^n(cos(3*2^(r-1)beta))/(cos(2^r beta)),beta=36^@,` then

S (n) = sum_ (r = 1) ^ (n) ((cos (2 * 3 ^ (r-1) alpha)) / (sin (3 ^ (r) alpha), alpha = 18 ^ (@) ) and P (n) = sum_ (r = 1) ^ (n) (cos (3 * 2 ^ (r-1) beta)) / (cos (2 ^ (r) beta)), beta = 36 ^ ( @)

Find the sum sum_(r=1)^(n)(cos((2r-1)pi))/((2n+1))

sum_(r=1)^(n-1)cos^(2)""(rpi)/(n) is equal to

Find the sum of sum_(r=1)^(n)cos(((2r-1)pi)/(2n+1))

Evaluate sum_(r=1)^(n-1) cos^(2) ((rpi)/(n)) .

Evaluate sum_(r=1)^(n-1) cos^(2) ((rpi)/(n)) .

For x in(0,(pi)/(4)). Let S_(n)=sum_(r=1)^(2n)sin(sin^(-1)x^(3r-2)),C_(n)=sum_(r=1)^(2n)cos(cos^(-1)x^(3r-1)) and T_(n)=sum_(r=1)^(2n)tan(tan^(-1)x^(3r)) where n in N and n>=3

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to

sum_(r=1)^(n)r^(3)=f(n) then sum_(r=1)^(n)(2r-1)^(3) is equal to