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 _________.

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)/(4)sum_(n=1)^(oo)P_(n)^((1)/(n)) is

Let a_n= 16,4,1,… be a geometric sequence .Define P_n as the product of the first n terms. The value of Sigma_(n=1)^(oo) nsqrtP_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.

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

The first term of a geometric sequence is 64, and the common ratio is (1)/(4) . For what value of n is t_(n)=(1)/(4) ?

Write the first three terms of the sequence a_n=(-1)^(n-1)5^(n+1) .

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) =

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

Write the first three terms defined by a_n= n/(n+1)