Use the Integral Test to Investigate the Series $\sum_{\mathrm{n}=1}^{\infty} \frac{1}{\mathrm{n}^{3 / 2}}$

Multiple Choice

Use the integral test to investigate the series $\sum_{\mathrm{n}=1}^{\infty} \frac{1}{\mathrm{n}^{3 / 2}}$ .

A) The integral $\int_{1}^{\infty} \frac{1}{x^{3 / 2}} d x=2$ , so the series $\sum_{n=1}^{\infty} \frac{1}{n^{3 / 2}}=2$ .
B) The integral $\int_{1}^{\infty} \frac{1}{\mathrm{x}^{3 / 2}} \mathrm{dx}=2$ , so the series $\sum_{\mathrm{n}=1}^{\infty} \frac{1}{\mathrm{n}^{3 / 2}}$ converges.
C) The integral $\int_{1}^{\infty} \frac{1}{\mathrm{x}^{3 / 2}} \mathrm{dx}=2$ , so the series $\sum_{\mathrm{n}=1}^{\infty} \frac{1}{\mathrm{n}^{3 / 2}}$ diverges.
D) The integral $\int_{1}^{\infty} \frac{1}{x^{3 / 2}} d x=2$ , so the test fails to tell us anything about the series.