Aymara Gallardo, Graduate Assistant at New Mexico State University, Numerade Educator

05:26

Calculus of a Single Variable

Graphical Analysis In Exercises 3 and $4,$ the figures show the graphs of the first 10 terms, and the graphs of the first 10 terms of the sequence of partial sums, of each series.

(a) Identify the series in each figure.
(b) Which series is a $p$ -series? Does it converge or diverge?
(c) For the series that are not p-series, how do the magnitudes of the terms compare with the magnitudes of the terms of the $p$ -series? What conclusion can you draw about the convergence or divergence of the series?
(d) Explain the relationship between the magnitudes of the terms of the series and the magnitudes of the terms of the partial sums.
$\sum_{n=1}^{\infty} \frac{2}{\sqrt{n}}, \quad \sum_{n=1}^{\infty} \frac{2}{\sqrt{n}-0.5}$, and

$$\sum_{n=1}^{\infty} \frac{4}{\sqrt{n+0.5}}$$

Chapter 9: Infinite Series

Section 4: Comparisons of Series