Sum of infinite series

Algebra Level 2

Use the approximation π = 22 7 \pi = \dfrac{22}7 , express the series below as a rational number. 1 + 1 π + 1 π 2 + 1 π 3 + ⋯ 1 + \dfrac1\pi + \dfrac1{\pi^2} + \dfrac1{\pi^3} + \cdots

22 15 \frac{22}{15} 7 15 \frac7{15} 22 7 \frac{22}7 15 7 \frac{15}7

Srinivasa Gopal by Srinivasa Gopal , 53, India

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1 solution

Srinivasa Gopal
Oct 3, 2018

Sum of an infinite series with |r| is a/1-r where r is the common ratio and a is the first term.

In the above infinite series a = 1 and r = 1/pi therefore a/1-r is equal to 1/ ( 1 - 7/22) = 22/15.

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