Calculus 2

Try using the integral test on your own for the series $\sum_{n=1}^{\infty} e^n$ and determine if it converges or diverges.

If you look at the improper interval and the improper integral converges or diverges, whatever it does, the same is true of the series.

Calculate whether the series $\sum_{n=1}^{\infty} \frac{1}{n^2}$ is convergent using the integral test, and estimate its sum.

Using the comparison test, determine if the series $\displaystyle \sum_{n=1}^{\infty} \frac{1}{2^n + 1}$ is convergent by comparing it to the series $\displaystyle \sum_{n=1}^{\infty} \frac{1}{2^n}$.

Determine whether the series $\displaystyle \sum_{n=1}^{\infty} \frac{5}{2n^2 + 4n + 3}$ is convergent using the comparison test.

Determine whether the series represented by the function is convergent or divergent using the integral test for the function: $\displaystyle \int_{1}^{\infty} \frac{1}{2^x} \, dx$

Determine whether the series represented by the function is convergent or divergent using the integral test for the function: $\displaystyle \int_{1}^{\infty} \frac{x}{x^2 + 1} \, dx$