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Q. 3TF

Expert-verifiedFound in: Page 617

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

An Improper Integral and Infinite Series: Sketch the function $f\left(x\right)=\frac{1}{x}$ for x ≥ 1 together with the graph of the terms of the series $\sum _{k=1}^{\infty}\frac{1}{k}.$ Argue that for every term ${S}_{n}$ of the sequence of partial sums for this series,${S}_{n}>{\int}_{1}^{n+1}\frac{1}{x}dx$. What does this result tell you about the convergence of the series?

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