Variance of the group `alpha, alpha + 2, alpha + 4, alpha + 6,.......`upto n terms `(alpha!=0)` is

Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + ... to n terms.

The variance of observation x_(1), x_(2),x_(3),…,x_(n) is sigma^(2) then the variance of alpha x_(1), alpha x_(2), alpha x_(3),….,alpha x_(n), (alpha != 0) is

The variance of observation x_(1), x_(2),x_(3),…,x_(n) is sigma^(2) then the variance of alpha x_(1), alpha x_(2), alpha x_(3),….,alpha x_(n), (alpha != 0) is

If a variable takes the discrete values : alpha + 4, alpha - (7)/(2), alpha - (5)/(2), alpha - 3, alpha - 2, alpha + (1)/(2), alpha - (1)/(2), alpha + 5, (alpha gt 0) , then the median is :

If n=(pi)/(4 alpha), then tan alpha tan2 alpha tan3 alpha.......tan(2n-1)alpha is equal to

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

Find the sum to n terms of the following series: cos alpha + cos (pi - alpha) + cos (2pi + alpha) + .......(0 < alpha < (pi)/2) .