## Related questions with answers

Question

Use the geometric series

$f ( x ) = \frac { 1 } { 1 - x } = \sum _ { k = 0 } ^ { \infty } x ^ { k }$

, for |x|<1, to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.

Solution

VerifiedAnswered 10 months ago

Answered 10 months ago

Step 1

1 of 4$\color{#c34632}Solution:$

We need to find the power series representation for the following function (centered at 0): $\color{#4257b2}f(-4x)=\dfrac{1}{1+4x}$ and later on, its raduis and interval of convegence.

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