Let Sn = n Σ k-1 √k Estimate how many terms are required before sn ≥ 100.
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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Analysis
Transcribed Image Text:Let Sn
-
n
Σ Estimate how many terms are
k=1
1
√k
required before sn ≥ 100.
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Follow-up Question
Why does it equal 1+(n^2 - 1)/n?
![The equation shown is:
\[
1 + \left( \frac{1}{n} + \frac{1}{n} + \cdots + \frac{1}{n} \right) = 1 + \frac{n^2 - 1}{n}
\]
Explanation:
- The expression \(\left( \frac{1}{n} + \frac{1}{n} + \cdots + \frac{1}{n} \right)\) implies that the term \(\frac{1}{n}\) is repeated. It's assumed to be repeated \(n\) times, based on the algebraic simplification shown on the right side of the equation.
- The right side simplifies the repeated addition as a single fraction: \(\frac{n^2 - 1}{n}\).
This equation illustrates the summation of \(n\) identical fractions and its algebraic simplification.](https://content.bartleby.com/qna-images/question/3ada9a20-cfc4-4295-96e5-fd4aa8bf1cec/d519d349-6d4a-41b4-a5b8-8f5390a18ccb/dltpux8_processed.png)
Transcribed Image Text:The equation shown is:
\[
1 + \left( \frac{1}{n} + \frac{1}{n} + \cdots + \frac{1}{n} \right) = 1 + \frac{n^2 - 1}{n}
\]
Explanation:
- The expression \(\left( \frac{1}{n} + \frac{1}{n} + \cdots + \frac{1}{n} \right)\) implies that the term \(\frac{1}{n}\) is repeated. It's assumed to be repeated \(n\) times, based on the algebraic simplification shown on the right side of the equation.
- The right side simplifies the repeated addition as a single fraction: \(\frac{n^2 - 1}{n}\).
This equation illustrates the summation of \(n\) identical fractions and its algebraic simplification.
Solution
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