Q. 3TF - Calculus

Question

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?

Step-by-Step Solution

Answer

a

Step 1. Given Information.

a

Step 2.

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