SOLUTION: I'm not quite sure what this means... Find the sum of the infinite geometric series: .8+.08+.008 PLEASE help! thanks <3

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I'm not quite sure what this means... Find the sum of the infinite geometric series: .8+.08+.008 PLEASE help! thanks <3      Log On


   



Question 112572: I'm not quite sure what this means...
Find the sum of the infinite geometric series:
.8+.08+.008
PLEASE help! thanks <3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This infinite series is just another way of saying
.88888888888... on and on forever and ever. In the
problem, they just pulled out each 8, so they got
.8+%2B+.08+%2B+.008+%2B+.0008... on and on forever
Believe it or not, .88888888888... =8%2F9
You find it with a little trick.
First call the repeating decimal n.
Then show what 10n is
10n+=+8.88888888...
n+=+.888888888...
subtract n from 10n. Everything to the right of the
decimal points cancel out. I'm left with
9n+=+8
n+=+8%2F9answer
OK, what if you had .137137137137137... on and on and on?
What's the value? Use the same trick a little differently
1000n+=+137.137137137137...
n+=+.137137137137137...
now subtract
999n+=+137
n+=+137%2F999answer