# Is this a convergent series?

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1. Jul 10, 2015

### matthew1

Mod note: Moved from a homework section.
1. The problem statement, all variables and given/known data

this is my lecturer's notes, he says it is a divergent series, but this seems like an obvious convergent series to me..
could someone verify?

2. Relevant equations

https://www.dropbox.com/s/mc5rth0cgm94reg/incorrect maths.png?dl=0

3. The attempt at a solution

Last edited by a moderator: Jul 10, 2015
2. Jul 10, 2015

### SammyS

Staff Emeritus
The series is the sum of all of the terms of the sequence. The sequence does converge to 2.

What is the sum of an infinite number of terms each of which is at least a little greater than 2 ?

3. Jul 10, 2015

### matthew1

Ah, I thought i was already looking at the series, but that was the terms of the sequence! thanks a lot :-)

4. Jul 10, 2015

### mathman

5. Jul 10, 2015

### Staff: Mentor

Be sure you learn the difference between a sequence of terms, such as $\{2 + e^{-m}\}_{m = 1}^{\infty}$, and a series, such as $\sum_{m = 1}^{\infty}2 + e^{-m}$.