# Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it: 12,14,18,116, ... - Mathematics and Statistics

Sum

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

1/2, 1/4, 1/8, 1/16, ...

#### Solution

1/2, 1/4, 1/8, 1/16, ...

Here, "a" = 1/2, "r" = (1/4)/(1/2) = 1/2

Since, | r | = |1/2| < 1

∴ Sum to infinity exists.

Sum to infinity = "a"/(1 - "r") = (1/2)/(1 - 1/2) = 1.

Concept: Sum of Infinite Terms of a G. P.
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.3 | Q 1. (i) | Page 56