Consider the following repeating decimal. 0.417 (a) Write the repeating decimal as a geometric series. 0.417 = 0.4 + ∞ n = 0 0.017 (b) Write the sum of the series as the ratio of two integers. 413/990 1/10
Consider the following repeating decimal. 0.417 (a) Write the repeating decimal as a geometric series. 0.417 = 0.4 + ∞ n = 0 0.017 (b) Write the sum of the series as the ratio of two integers. 413/990 1/10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the following repeating decimal.
\[ \overline{0.417} \]
(a) Write the repeating decimal as a geometric series.
\[ \overline{0.417} = 0.4 + \sum_{n=0}^{\infty} 0.017 \left( \frac{1}{10} \right)^n \]
(b) Write the sum of the series as the ratio of two integers.
\[ \frac{413}{990} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83f79971-d8c7-47c2-a088-4cbb2ca092fe%2F60375bfb-e28c-4dfa-8995-33a82f5e2619%2F100jurn_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following repeating decimal.
\[ \overline{0.417} \]
(a) Write the repeating decimal as a geometric series.
\[ \overline{0.417} = 0.4 + \sum_{n=0}^{\infty} 0.017 \left( \frac{1}{10} \right)^n \]
(b) Write the sum of the series as the ratio of two integers.
\[ \frac{413}{990} \]
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