Problem

Determine whether the series converges or diverge…

03:14

Problem 7 Easy Difficulty

Determine whether the series converges or diverges.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {9^n}{3 + 10^n} $

Answer

Converges

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 4

The Comparison Tests

Discussion

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Video Transcript

so first weaken it. Looking at the earth term of the series. So this is equipment. Teo, This serious when n is large enough? Yeah, And we know that this is gonna be committees. Actually, we can compute its limits. This is equal to when there were one minus. No, I know it. Ten. So this is equal to ten, and we know that. So this is the first method, and cig matter is very easy to observe that So for each term, the serious would say in this less than being which is this one. And we know the beings converted convergent. So we conclude that in convergence

Yiming Z.

University of Illinois at Urbana-Champaign