How do we know when a sum of a series its geometric ?

Question

jhannybean · Answer

You have a common ratio between all the values, as compared to a difference, and $|r|<1$

triciaal · Answer

is the question worded properly? 
do you mean when a series is a sum or geometric?

jhannybean · Answer

When you divide the first term by the second, second by the third, etc, you have a common proportion between each of the terms.

jhannybean · Answer

ex: $\sf 10, 30, 90, 270...$$$\frac{30}{10} = 3$$$$\frac{90}{30} = 3$$$$\frac{270}{90}=3$$

anonymous · Answer

$$\sum_{n=0}^{\infty}[-2]^n[e^-n]$$ so for example if you have an equation like this how would you know when to use geometric series or alternating series. If you are try to prove convergence or divergence?

jhannybean · Answer

@ganeshie8 ? :\

campbell_st · Answer

the easiest thing to do is find the first few terms then make a decision. 

substitute n = 1, then n = 2 and n = 3 etc

look to see what is happening... 

I'm insure if its 

$$e^n ~~or~~e_{n}$$

or some other term