Question

Does the infinite geometric series diverge or converge, if it has a sum what is it? Explain.

3 + 9 + 27 + 81 + ...

Answer 1

\[\sum_{n=0}^{\infty}3n\]

Answer 2

that should be n = 1

it clearly doesn't converge,

http://tutorial.math.lamar.edu/Classes/CalcII/Series_Basics.aspx

Answer 3

doesnt really matter though

Answer 4

Read these notes they are fairly good

https://www.wolframalpha.com/input/?i=n%3D1++summation+infinity+3n

Answer 5

Since it diverges it has no sum? Does this hold true for everything?
Converge = Sum
Diverge = No sum

Answer 6

Convergence is when a series has a fixed value when completely added

Divergence is when that sum is infinity

Answer 7

Since infinity is a concept and not a number it does not have a sum

Answer 8

Ok. Thanks :)

Answer 9

You should check out this video, https://www.youtube.com/watch?v=u7Z9UnWOJNY

Answer 10

It relates to calculus 2