Question

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. (If the series is divergent, enter DIVERGENT.)

(1)-(1/6)+(1/36)-(1/216)+...

Answer 1

absolutely converges

Answer 2

How do I find the sum? I have no idea.

Answer 3

r=- 1/6

Answer 4

1
-------------
1 - -1/6

Answer 5

that doesn't work

Answer 6

\[\huge {\color{DarkRed} {It\: doesent}}\]

Answer 7

1/ 7/6 = 6/7

Answer 8

Nope!

Answer 9

Everyone please HELP!

Answer 10

The geometric series given is \[\sum_{n=0}^{\infty} (\frac{-1}{6})^n\]
Which clearly converges since \(|-\frac{1}{6}|<1\).

Answer 11

I'm sure you have the formula and can find the sum.

Answer 12

http://www.wolframalpha.com/input/?i=Sum%5B(-6%5E(-1))%5En%2C%20%7Bn%2C%200%2C%20Infinity%7D%5D&t=crmtb01

Answer 13

So is it -1/6? If it is, my hw program says it's wrong.

Answer 14

The answer is 6/7

Answer 15

What's \(-\frac{1}{6}?\) The sum is not -1/6.

Answer 16

it marked it wrong though!

Answer 17

did you put 6/7?

Answer 18

YEP!

Answer 19

then I don't know what to say, 6/7 is correct answer

Answer 20

im with imran. that is really the correct answer.

Answer 21

Huh... I trust you guys. I guess there might be a glitch in the program then.

Answer 22

GOT IT!!! Thank you :D

Answer 23

Can you help me with this one?

The tenth term of an arithmetic sequence is (57/2), and the second term is (9/2). Find the first term.

Answer 24

9/2 + d (8)=57/2

find d

Answer 25

subtract d from 9/2

Answer 26

So D=3?