I tried graphing it with a really huge n number to get an idea on how it may look, and the graph mirrors nothing. Im totally stuck, to be I no considering a theorem?

The collection

\$\$sum_n = 1^infty frac2^nx^n = sum_n = 1^infty left(frac2x ight)^n\$\$

is a geometric collection with initial term \$2/x\$ and also common ratio \$2/x\$.

A geometric collection with a non-zero initial hatchet converges as soon as the common ratio has absolute value less than \$1\$.

You could likewise apply the ratio Test, which leads to the very same result, return you have actually to check that the collection diverges once \$x = pm 2\$.

You are watching: Find all values of x for which the series converges

Hint 1 : Look at \$\$sum_n=1^infty (frac2x) ^n\$\$

which is the exact same sum.

Hint 2 : The given collection is a geometric series.

Thanks for contributing response to urbanbreathnyc.com Stack Exchange!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; back them increase with recommendations or personal experience.

Use urbanbreathnyc.comJax to format equations. urbanbreathnyc.comJax reference.

See more: The First Step In Activity Based Costing Is To, The First Step In Activity

To find out more, view our tips on writing great answers.

## Not the price you're looking for? Browse other questions tagged sequences-and-series or asking your very own question.

site design / logo design © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.20.40515

urbanbreathnyc.comematics ridge Exchange works best with JavaScript permitted