MHB Solving Series Limit Problem: Find Convergence/Divergence

  • Thread starter Thread starter tmt1
  • Start date Start date
  • Tags Tags
    Limit Series
Click For Summary
The discussion centers on determining the convergence or divergence of the infinite series $$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$. Participants suggest using the formula for infinite geometric series, which converges if the common ratio is between -1 and 1. In this case, since $$\frac{e}{3}$$ is less than 1, the series converges. The convergence can be confirmed by applying the geometric series test. The series converges to a specific value based on this analysis.
tmt1
Messages
230
Reaction score
0
I have this limit:

$$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$

Which method can I use to find if it converges or diverges?
 
Physics news on Phys.org
tmt said:
I have this limit:

$$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$

Which method can I use to find if it converges or diverges?

Look up infinite geometric series.
 

Similar threads

I Infinite Series - Divergence of 1/n question
  • · Replies 5 ·
Replies
5
Views
2K
I Understanding the nth-term test for Divergence
  • · Replies 17 ·
Replies
17
Views
5K
B Understanding about Sequences and Series
  • · Replies 3 ·
Replies
3
Views
2K
I How does the ratio test fail and the root test succeed here?
  • · Replies 6 ·
Replies
6
Views
3K
A Solving a power series
  • · Replies 3 ·
Replies
3
Views
3K
B Difficulty with understanding whether 1/n converges or diverges
  • · Replies 11 ·
Replies
11
Views
5K
I What is the difference between these two power series theorems?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Series Convergence Or Divergence
  • · Replies 1 ·
Replies
1
Views
2K
MHB 11.6.8 determine convergent or divergence by Ratio Test
  • · Replies 3 ·
Replies
3
Views
2K
MHB Determining the convergence or divergence of a sequence using comparison test
  • · Replies 3 ·
Replies
3
Views
2K