Question

HELP???

Answer 1

If you write the series out, you get:

-4*(1/3)^0 + -4*(1/3)^1 + -4*(1/3)^2 + -4*(1/3)^3 + ....

So you can calculate the first 4 terms, I think...

Answer 2

THe factor 1/3 tells you if it converges or diverges. What do you think?

Answer 3

It means: if it has a limit ( such as 10 in the other series), then it converges.
If it goes to infinity, it diverges.
E.g: 2*3^n diverges, because it is 2 + 6 + 18 + 54 + ...
Every term is much bigger than the last one, so adding everything goes wrong...

Answer 4

If you have to start with n=1, then it still comes out as -4*(1/3)^0, because there is n-1 in the formula!

Answer 5

Yes!

A geometric series converges if |r| < 1, it diverges if |r| >= 1.

Answer 6

If it converges, it has a sum.
Formula for the sum:

s =a(1-r)

a = -4,
r = 1/3

Answer 7

Make that a/(1-r)

Answer 8

-4.3333333

Answer 9

Yes, they are correct...

Answer 10

Now what is the sum?

Answer 11

-4.3333333

Answer 12

s = a/(1-r)

Answer 13

ohh

Answer 14

s=a/(1-r)=-4*(1-1/3)=-4/(2/3)=-4*3/2=-12/2=-6

Answer 15

oh opps! Ok i get it !

Answer 16

thanks sooomuch!

Answer 17

YW!