Calculus 2: Series and the integral test

Determine if the infinite series $\sum_{n=1}^{\infty} \frac{5n+3}{7n-4}$ converges or diverges using the divergence test.

Using the summation notation $\Sigma$, calculate the sum of the geometric series from $k=2$ to $k=7$ with the geometric rule $a_k = \frac{1}{2}^k \times 2$.

Evaluate whether a geometric series with terms A times R^(N-1) is convergent or divergent given different values of R.

Explore whether the infinite series from n equals 1 to infinity of $\frac{1}{n^2}$ converges or diverges using the integral test.

For a series represented with a corresponding function over an interval, use the integral test to determine convergence.

Apply divergence test to a series where the sequence does not converge to zero, such as one involving logarithmic terms.

Use the integral test to determine if the series $\displaystyle \sum_{n=1}^{\infty} \frac{n}{n^2 + 1}$ converges or diverges.

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

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

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: $\displaystyle \int_{1}^{\infty} \frac{x}{x^2 + 1} \, dx$