Question

A repeating decimal expansion such as x = 5.78787878 can be interpreted as the infinite geometric series x = 5 + 78/10^2 + 78/10^4 + 78/10^6 + . . . . By summing this infinite geometric series we thus get the rational number having the given repeating decimal expansion. Use this idea to find the rational number r whose repeating decimal expansion is 2.52525252 .

          A repeating decimal expansion such as

x = 5.78787878

can be interpreted as the infinite geometric series

x = 5 + 78/10^2 + 78/10^4 + 78/10^6 + . . . .

By summing this infinite geometric series we thus get the rational number having the given repeating decimal expansion.
Use this idea to find the rational number r whose repeating decimal expansion is

2.52525252 .

A repeating decimal expansion such as

x = 5.78787878

can be interpreted as the infinite geometric series

x = 5 + 78/10^2 + 78/10^4 + 78/10^6 + . . . .

By summing this infinite geometric series we thus get the rational number having the given repeating decimal expansion.
Use this idea to find the rational number r whose repeating decimal expansion is

2.52525252 .

Added by Donald P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Moses Obasola

04/06/2022

Step 1

52525252... Multiplying X by 100, we get 100X = 252.52525252... Subtracting X from 100X, we get: 99X = 250 X = 250/99 Show more…

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A repeating decimal expansion such as x = 5.78787878 can be interpreted as the infinite geometric series x = 5 + 78/10^2 + 78/10^4 + 78/10^6 + . . . . By summing this infinite geometric series we thus get the rational number having the given repeating decimal expansion. Use this idea to find the rational number r whose repeating decimal expansion is 2.52525252 .