Multiple choice

The sum of the infinite series 1 + 2/3 + 4/9 +......... is

  1. 1/3

  2. 3

  3. 2/3

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an infinite geometric series with first term a = 1 and common ratio r = 2/3. The sum of an infinite GP is S = a/(1-r) when |r| < 1. Here, S = 1/(1 - 2/3) = 1/(1/3) = 3. The series converges because 2/3 < 1.

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