Let a_n=16,4,1,…… be a geometric sequence. The value of ∑n=1∞P_nn, where P_n is the product of the first n terms, is equal to

Question

Let a_n=16,4,1,…… be a geometric sequence. The value of ∑n=1∞P_nn, where P_n is the product of the first n terms, is equal to.

MARKS Content Team · Accepted Answer

Correct answer: (C) 32. For the G.P. a,ar,ar^2,……… P_n=aarar^2…..ar^(n-1) =a^nr^(nn-12) ⇒P_nn=ar^(n-12) ⇒∑n=1∞P_nn=a1+√r+r+r√r+.…… =a/(1-√r) Given, a=16 and r=1/4 =16/(1-√14)=32

Let $a_{n} = 16, 4, 1, \dots \dots$ be a geometric sequence. The value of $\sum_{n = 1}^{\infty} \sqrt[n]{P_{n}},$ where $P_{n}$ is the product of the first $n$ terms, is equal to.

Solution

More Sequences and Series Questions

Let an=16,4,1,…… be a geometric sequence. The value of ∑n=1∞Pnn, where Pn is the product of the first n terms, is equal to.

Solution

More Sequences and Series Questions

Let $a_{n} = 16, 4, 1, \dots \dots$ be a geometric sequence. The value of $\sum_{n = 1}^{\infty} \sqrt[n]{P_{n}},$ where $P_{n}$ is the product of the first $n$ terms, is equal to.