Question

I'm looking to determine the convergence or divergence of the geometric series E^(infinity)_ j =1. 4(-1/3)^j-1.
*that is the autosome of j to infinity*

Answer 1

I don't speak French, sorry.

Answer 2

Where are you from? I judged that by your name...

Answer 3

The US. (Imported)

Answer 4

From?

Answer 5

Mexico

Answer 6

Porque yo no entiendo lo que escribite tu...

Answer 7

Es \(\large\sum\limits_{j=1}^\infty \left[4(-\frac13)^j-1\right]\) lo que significas?

Answer 8

That's the one! How do you enter graphics?

Answer 9

I don't have the autosum key

Answer 10

So you don't speak Spanish?

I learnt \(\LaTeX\) by myself, here is what I typed:

\(\mbox{\ }\mbox{(}\) \sum_{j=1}^\infty \left[ 4(-\frac13)^j -1 \right] \(\mbox{\ )}\mbox{}\)

Answer 11

That's awesome, thanks. As far as speaking Spanish, I'm second- generation import, and didn't learn a lot of spanish. I'm actually learning, now, but I understand it mostly.

Answer 12

I see. Try to learn \(\LaTeX\), it can help you a lot :)

\ (\LaTeX\ ) --> \(\LaTeX\)

Answer 13

\ (\sum_{j=1}^1\infty\left[4(-frac13)^j-1\right]\)

Answer 14

(needs practice )

Answer 15

so when i'm displaying the code I would leave a gap between \ and (
but when you really need to type the code out, don't.

Answer 16

By the way, \ and ( is for in-line, while \ and [ will give you a newline

Answer 17

Thanks for these tips!

Answer 18

no problem :)

Answer 19

So you're in an English-speaking country, with a Spanish-speaking origin, and a French surname?!

Answer 20

Wait, is Ramosville your surname

Answer 21

Haha, all of the Ramos-usernames were taken. So I went with Ramos-ville. Its from the song Margaritaville

Answer 22

oh lol

Answer 23

Sweet, thanks for the medal!

Answer 24

\[\lim_{j\rightarrow\infty}\frac{\left[ 4(-\frac13)^{j+1} -1 \right]}{\left[ 4(-\frac13)^j -1 \right]}\]

\ [\lim_{j\rightarrow\infty}\frac{\left[ 4(-\frac13)^{j+1} -1 \right]}{\left[ 4(-\frac13)^j -1 \right]}\]

Answer 25

So this formula is what is used to determine convergence?

Answer 26

What is your background in math? You seem pretty sharp

Answer 27

yep, and my father taught me much about math

Answer 28

So you teach, or do this for fun?

Answer 29

Look at my profile, I'm just 14 years old, how can i teach lol

Answer 30

Wow, that is amazing. You are making your father proud.

Answer 31

Gracias :)

Answer 32

Y tu, cuantos anos tienes?

Answer 33

I am old! Hey, I had one quick question ! How did you arrive at that formula?

Answer 34

https://en.wikipedia.org/wiki/Ratio_test#The_test

Answer 35

Great, thank you for all your help. You have a bright future, young friend.

Answer 36

No problem and thank you :)