Let `a_n=16 ,4,1, ` be a geometric sequence. Define `P_n` as the product of the first `n` terms. Then the value of `1/4sum_(n=1)^oo P_n^(1/n)` is _________.

The value of sum_(n=1)^(oo)(4n-2)/(3^(n))

Let a_(n)=16,4,1,……….. be a geometric sequence. The value of Sigma_(n=1)^(oo)rootn(P_(n)) , where P_(n) is the product of the first n terms, is equal to.

Write the first five terms of the sequence defined by a_(n)=(-1)^(n-1).2^(n)

Let a_n , n ge 1 , be an arithmetic progression with first term 2 and common difference 4. Let M_n be the average of the first n terms. Then the sum_(n=1)^10 M_n is

Let P_(n) denote the product of first n terms of the G.P. 16, 4, 1, 1/4,…., then overset(oo)underset(n=1)Sigma (P_(n))^(1//n) =

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1) to (2n) terms is (1)/(r^(n))

the sum of the n terms of A.P. is 4n(n-1) then the sum of their squares is:

Show that the ratio of the sum of first n terms of a G.P. and the sum of (n+1)th term to (2n)th term is (1)/(r^(n)) .

In a sequence, if S_n is the sum of n terms and S_(n-1) is the sum of (n-1) terms, then the nth term is _________.

Find the sum of the first n terms ofthe sequence: 1+2(1+(1)/(n))+3(1+(1)/(n))^(2)+4(1+(1)/(n))^(3)+