Question

We can re-write $\frac{1}{4}(\frac{x}{4})^n$ as $(\frac{x^n}{4^{n+1}})$. Therefore, $f(x) = \frac{1}{4} \sum_{n=0}^{\infty} (-1)^n (\frac{x}{4})^n$ is equivalent to the following. $f(x) = \sum_{n=0}^{\infty} ()$

          We can re-write $\frac{1}{4}(\frac{x}{4})^n$ as $(\frac{x^n}{4^{n+1}})$.
Therefore, $f(x) = \frac{1}{4} \sum_{n=0}^{\infty} (-1)^n (\frac{x}{4})^n$ is equivalent to the following.
$f(x) = \sum_{n=0}^{\infty} ()$

We can re-write (1)/(4)((x)/(4))^n as ((x^n)/(4^n+1)).
Therefore, f(x) = (1)/(4)∑n=0^∞ (-1)^n ((x)/(4))^n is equivalent to the following.
f(x) = ∑n=0^∞ ()

Added by Deborah M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/23/2023

Step 1

Step 1: The expression $\frac{1}{4} \left( \frac{x}{4} \right)^n$ can be rewritten as $\left( \frac{x^n}{4^{n+1}} \right)$. Show more…

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We can re-write $\frac{1}{4} \left( \frac{x}{4} \right)^n$ as $\left( \frac{x^n}{4^{n+1}} \right)$. Therefore, f(x) = $\frac{1}{4} \sum_{n=0}^{\infty} (-1)^n \left( \frac{x}{4} \right)^n$ is equivalent to the following. $f(x) = \sum_{n=0}^{\infty} \left( \boxed{ \frac{(-1)^n x^n}{4^{n+1}} } \right)$