💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# Find the Maclaurin series for $f(x)$ using the definition of a Maclaurin series. [ Assume that $f$ has a power series expansion. Do not show that $R_n (x) \to 0.$] Also find the associated radius of convergence.$f(x) = 2^x$

## $f(x)=\sum_{n=0}^{\infty} \frac{(\ln 2)^{n} x^{n}}{n !} ,\quad R=\infty$

Sequences

Series

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

when they used the definition to show a fax to expend efforts as is Meckler and serious at point as equals Europe. Okay, so what is the definition of Meckler is yours effects at off FX at zero there's going to be signal inform zeroed in Philly the intuitive of f of x zero. So that's gonna be zero terms except Horace And there were in Vitoria All right, so a prime equals to two for the ads times one two And we do it eternally. We're going to find at to the risk of acrobats equals two to the X Times one two, the power of in. So we're gonna fund So this value is going to be two zero It's one and it's so simply wanted to end. So if X is going to be, I want you to the end times X to the end or Victoria and the rigors of convergence is gonna be or rico's infinity. So the converters for for every real number

University of Illinois at Urbana-Champaign

Sequences

Series

Lectures

Join Bootcamp