# Determine whether the sum to infinity of the following G.P.s exist, if exists find them: 2,43,89,1627,... - Mathematics and Statistics

Sum

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

2, 4/3, 8/9, 16/27, ...

#### Solution

2, 4/3, 8/9, 16/27, ...

"a" = 2, "r" = (4/3)/2 = 2/3, |"r"| < 1

∴ Sum to infinity exists.

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

= 2/(1 - 2/3)

= 6

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Sequences and Series
Exercise 2.3 | Q 1. (ii) | Page 33