Mathematical Scratchpad

Practices on Power Series

  1. Find the interval of convergence for the following power series. [Be sure to check the convergence at the end points.]

    1. MATH

    2. MATH

  2. If MATH Find the power series for $f$ and find its interval of convergence.

  3. If MATH

    1. Find the power series for $f$ and find the interval of convergence.

    2. Find the power series for $\ln (1+x)$ and find the interval of convergence. [hint: $\ln (1+x)$ is the antiderivative of $f(x)$. ]

  4. Find the power series for $\dfrac{x}{1+x^{2}}$ and indicate its interval of convergence.

  5. If MATH find the power series for $g(x).$

  6. Use series to approximate MATH up to three decimal places.

  7. Find the power series for MATH (hint: MATH )

  8. Find the power series for MATH

  9. Find the Maclaurin series for $\sqrt{1+x}$ by hand.

  10. Find the first four nonzero terms of the Maclaurin series for MATH