SOLUTION: Another problem I need a little help with. Find the sum of the infinite geometric series if possible. -1+(1/4)-(1/16)+(1/64).... I multiplied by 4 and came up with 4s=-4+1-(1/4)

Question 65740: Another problem I need a little help with.
Find the sum of the infinite geometric series if possible.
-1+(1/4)-(1/16)+(1/64)....
I multiplied by 4 and came up with 4s=-4+1-(1/4)+(1/16). What do I do next? Or maybe it's not possible to find the sum.....???
Thanks
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:

Find the sum of the infinite geometric series if possible.
-1+(1/4)-(1/16)+(1/64)....

ANSWER:

Here the series is, -1+(1/4)-(1/16)+(1/64)....

We can see that first term is -1 and common ratio is -1/4
(you can find out common ratio of this series by dividing second term by third term)

Sum to infinity of a geometric seriesn is given by the formula,

S = a/(1-r) where 'a' is the first term and 'r' is the common ratio.

So we have,

S = -1/( 1-{-1/4} )

==> S = -1/( 1+{1/4} )

==> S = -1/( 1*4 +1)/4

==> S = -1/ (5/4)

==> S = -4/5

Which is the required answer.

Hope you understood.

Regards.

Praseena.

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