If `u_1,u_2,u_3,...` forms a G.P with common ratio `k` then find the sum of `u_1u_2+u_2u_3+...u_n+u_(n+1)` in terms of `u_1` and `k`

If u_(1), u_(2), u_(3),… form a G.P. with common ratio k, find the sum of u_(1)u_(2) + u_(2)u_(3)+….+u_(n)u_(n+1) in terms of u_(1) and k.

If u_n = 2cos n theta then u_1u_n - u_(n-1) is equal to

Find sum_(n=1)^n u_n if u_n=sum_(n=0)^n1/2^n .

If u_(n) = cos^(n) alpha + sin^(n) alpha , then the value of 2 u_(6) - 3 u_(4) +1 is :

If u_n=1/n-1/(n+1) , then u_1+u_2+u_3+u_4+u_5 is :

If u_(n)=2Cos^(n) theta then show that u_(1)u_(n)-u_(n-1)= u_(n+1)

If u_(1), u_(2), u_(3) "…..." represent the speed of n_(1), n_(2) , n_(3) ,"…..." molecules , then the root mean square speed is "____________" .