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. Find the power series for $\tan ^{-1}x$ by using MATH

  7. Find the power series for MATH

  8. Find the power series for MATH

  9. Find the power series for $e^{x}+e^{-x}.$

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