If `S=underset(k=1) overset(10)sum(sin""(2pik)/11-icos""(2pik)/11)` then

sum_(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

underset(r=0)overset(n)(sum)sin^(2)""(rpi)/(n) is equal to

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

If p=sum_(p=1)^(32)(3p+2)(sum_(q=1)^(10)(sin""(2qpi)/(11)-icos""(2qpi)/(11)))^(p) , where i=sqrt(-1) and if (1+i)P=n(n!),n in N, then the value of n is

overset(10)underset(i=3)sum5

Find the value of sum_(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wherei=sqrt(-1).

If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007! , then value of n is

underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-n^(2)) is equal to

Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset(10)sum tan^(-1) ((r)/(s))

If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n