Question

need help with this, use the geometric series test, from one to inifinty of (-3/2)^n, i got it was convergent, but just want to check my work

Answer 1

you do know that \[\frac{-3}{2} \cancel{\in} (-1,1)\]

Answer 2

?

Answer 3

see that, is where i dont understand, how do you know that, i have looked at samples of the geo test, but everytime i use it, i get it wrong, but i use the test correctly

Answer 4

how do i know the number -3/2 is not between -1 and 1?

Answer 5

yes, i see that

Answer 6

oh then what does "how do you know that" refer to?

Answer 7

how to show with the geometric test, like how do i show my work with that, not trying to make you do the work, just how do i prove that

Answer 8

r has to between -1 and 1 for it to converge

Answer 9

r being the common ratio

Answer 10

otherwise it diverges

Answer 11

that is the test

Answer 12

is it really that simple?

Answer 13

yep

Answer 14

then why do teachers make it so gosh dang more complicated

Answer 15

example
\[\sum_{n=1}^{\infty } (\frac{1}{2})^n \text{ this one converges because } \frac{1}{2} \in (-1,1)\]

Answer 16

example
\[\sum_{n=1}^{\infty} (\frac{-1}{2})^n \text{ also converges because } \frac{-1}{2} \in (-1,1)\]

Answer 17

so since that it is not between -1 and 1, it diverges

Answer 18

http://tutorial.math.lamar.edu/Classes/CalcII/Series_Special.aspx
don't know if you ever heard of pauls notes but he has really great notes :)

Answer 19

right

Answer 20

thank you, that makes a lot more sense, looking at notes and books, this is the easiest explanation i have heard

Answer 21

and no, i havent

Answer 22

usually books usually the inequality notation
maybe that seems harder to read that what the inequality actually means...

when it says:
\[\sum_{n=1}^{\infty}a (r)^n \text{ converges when } |r|<1 \\ \text{ the inequality is saying } -1<r<1 \\ \text{ or \in words everything between -1 and 1, exclusive }\]

Answer 23

exclusive meaning we are not including -1 and 1

Answer 24

anyways I'm glad it makes more sense now

Answer 25

thank you, so and pauls notes will have the other test im assuming

Answer 26

i'm pretty sure and i could be mistaken
paul's notes has everything you will need for calculus

Answer 27

again thank you

Answer 28

np