Question

PLEASE HELP(: Consider the infinite geometric series.

a. Write the first four terms of the series.
b. Does the series diverge or converge?
c. If the series has a sum, find the sum.

Answer 1

\[\sum_{n=1}^{infinity} -4 (1/3) ^ x-1

Answer 2

\[\sum_{n=1}^{infinity}\] -4 (1/3) ^x-1

Answer 3

\[\sum_{n=1}^{\infty} -4 \left(\frac{1}{3}\right)^ {x-1} \]?

Answer 4

certainly converges since \(-1<\frac{1}{3}<1\)

Answer 5

then use \(\frac{1}{1-\frac{1}{3}}\) to find the sum,
multiply by \(-4\) at the end

Answer 6

Yes that is the correct equation. Sorry I dont really know much about this website(:

Answer 7

the sum would be -6, Right? And how do I use that to find the other four terms in the series?

Answer 8

yes it would be -6

Answer 9

the first question is a direct computation
put in \(x=1\) then \(x=2\) etc

Answer 10

Into the equation with the sigma in it?

Answer 11

Can you tell me how to put that in the calcuator? Please(:

Answer 12

no it is asking only for the terms

Answer 13

\[-4\times (\frac{1}{3})^{1-1}=-4\times 0=-4\] is the first term

Answer 14

rather
\[-4\times (\frac{1}{3})^{1-1}=-4\times 1=-4\]

Answer 15

second term, replace \(x\) by 2 and get \(-4\times \frac{1}{3}=-\frac{4}{3}\) etc

Answer 16

So the third term is -4/9

Answer 17

and the fourth term is -4/27? correct?

Answer 18

Thank you so much(: You have been a life saver(: Do you know how trigonometric functions?

Answer 19

If you think you might can please take a look at this question.(: http://openstudy.com/study#/updates/50a53189e4b0329300a8d772