Use a graph to show that the inequality is true. What can you conclude about the

Chapter 9, Problem 56

(choose chapter or problem)

Use a graph to show that the inequality is true. What can you conclude about the convergence or divergence of the series? Explain.

(a) \(\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}\ >\ \int_1^{\infty}\frac{1}{\sqrt{x}}\ dx\)

(b) \(\sum_{n=2}^{\infty}\frac{1}{n^2}\ <\ \int_1^{\infty}\frac{1}{x^2}\ dx\)

Text Transcription:

sum_n=1 ^infty 1 / sqrt n > int_1 ^infty 1 / sqrt x dx

sum_n=2 ^infty 1 / n^2 < int_1 ^infty 1 / x^2 dx