Calculus 2

Approximate the sin function using a Taylor polynomial.

Using the ratio test, determine the intervals of convergence for the power series 28 29. Answer: The interval of convergence is $2 < x < 4$.

Determine the interval of convergence for the power series $\sum_{n=0}^{\infty} \frac{x^n}{n!}$ using the ratio test.

Determine the interval of convergence for the power series: $\sum \frac{1}{n} (x - 2)^n$.

Find the interval of convergence for the power series with $c_n = \frac{1}{n!}$ and $(x - 2)^n$.

Determine the radius of convergence for the power series with $c_n = n!$ and $(x - 2)^n$.

Express $\frac{1}{1 + x^2}$ as the sum of a power series.

Find the interval and radius of convergence for the power series representation of $\displaystyle \frac{1}{1+x^2}$.

Find a power series representation for $f(x)$ and determine the interval of convergence.

Express the function as a sum of a power series by first using partial fractions, then determine the interval of convergence.

Determine the interval of convergence for the series $\sum_{n=0}^{\infty} \frac{(-1)^n x^n}{4^{n+1}}$.

Use the root test to determine if the series $\left(\frac{3+5n}{2+3n}\right)^n$ converges, diverges, or is inconclusive.

Apply the root test to the series $\left(\frac{1}{n^2 + \frac{1}{n}}\right)^n$.

Use the root test on the series $\left(\frac{n^n}{2^{1+4n}}\right)$ to determine its convergence or divergence.

Determine if the series $\displaystyle \left(\frac{n}{2^n}\right)$ converges or diverges using the root test.

Apply the root test to the series $(-1)^n \cdot \frac{3^{n+2}}{(n-1)^n}$ to determine if it converges or diverges.

Using the Ratio Test or the Root Test, determine if the infinite series $\sum a_n$ converges or diverges.

Using the ratio test, determine if a given series converges or diverges.

Apply the root test to check if a series converges absolutely or diverges.

Using the ratio or root test, determine if the series [{ "type" : "katexPlugin", "text": "\sum a_n", "inline": true }]', is absolutely convergent.