Question

Find a power series representation for the following functions and where they are valid: \begin{enumerate} \item $\frac{1}{4+x}$ with center at $x=3$. \item $\frac{1}{(1+2x)^3}$ with center at $x=0$. \end{enumerate}

          Find a power series representation for the following functions and where they are valid:
\begin{enumerate}
    \item $\frac{1}{4+x}$ with center at $x=3$.
    \item $\frac{1}{(1+2x)^3}$ with center at $x=0$.
\end{enumerate}

Find a power series representation for the following functions and where they are valid:

* (1)/(4+x) with center at x=3.

* (1)/((1+2x)^3) with center at x=0.

Added by Andrew M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

12/12/2023

Step 1

.. In this case, we have r = -(x-3)/4. So, we can rewrite the function as: (1)/(4+x) = (1)/(4(1-(x-3)/4)) = (1/4)/(1-(x-3)/4) Now, we can rewrite this as a geometric series with r = (x-3)/4: (1)/(4+x) = (1/4) * (1 + (x-3)/4 + ((x-3)/4)^2 + ((x-3)/4)^3 + Show more…

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