`lim_(n->oo)sum_(k=1)^n((sin)pi/(2k)-(cos)pi/(2k)-(sin)(pi/(2(k+2))+(cos)pi/(2(k+2)))=`

sum_(k=1)^3 cos^(2)((2k-1)(pi)/(12))=

sum_(m=1)^(32)m[sum_(k=1)^(6)sin2k(pi)/(7)-i cos2k(pi)/(7)]

Let F(x)=(1+sin((pi)/(2k))(1+sin(k-1)(pi)/(2k))(1+sin(2k+1)(pi)/(2k))(1+sin(3k-1)(pi)/(2k)) The value of F(1)+F(2)+F(3) is equal to

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

Let F(x)=(1+sin(pi/(2k))(1+sin(k-1)pi/(2k))(1+sin(2k+1)pi/(2k))(1+sin(3k-1)pi/(2k)) . The value of F(1)+F(2)+F(3) is equal to

Evaluate lim_(ntooo)(1)/(n)[sin^(2k).(pi)/(2n)+sin^(2k).(2pi)/(2n)+....+sin^(2k).(pi)/(2)]