SOLUTION: Find the sum of the geometric series 1+1/3+4/9+8/9+...

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Question 1098493: Find the sum of the geometric series
1+1/3+4/9+8/9+...
Found 2 solutions by KMST, richwmiller:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1%2B1%2F3%2B4%2F9%2B8%2F9%2B%22...%22 is not exactly a geometric series
1%2B2%2F3%2B4%2F9%2B8%2F9%2B16%2F27%2B32%2F81%2B%22...%22 is a geometric series
with first term b=1 and common ratio r=2%2F3 .
For any geometric series with r%3C1 ,
the sum to infinity can be calculated as
S=b%2F%281-r%29 ,
so 1%2B2%2F3%2B4%2F9%2B8%2F9%2B%22...%22=1%2F%281-2%2F3%29=1%2F%281%2F3%29=3

If what you really want to calculate is
,
then
1%2B1%2F3%2B4%2F9%2B8%2F9%2B16%2F27%2B32%2F81%2B%22...%22=%28-1%2F3%29%2B3=2%262%2F3=8%2F3 .

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1+2/3+4/9+8/9+16/27+32/81+"..." is not a geometric series either.
4/9*2/3 doesn't equal 8/9