SOLUTION: find the sum of each of the following inifinite G.P's:
(a) 1 + 1/3 + 1/9 + 1/27 + +...
(b) 2/5 + 3/5^2 + 2/5^2 + 3/5^4...
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Question 1122511: find the sum of each of the following inifinite G.P's:
(a) 1 + 1/3 + 1/9 + 1/27 + +...
(b) 2/5 + 3/5^2 + 2/5^2 + 3/5^4...
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Th infinite sum of a geometric progression with common ratio between -1 and 1 is
where a is the first term and r is the common ratio.
(a) first term 1; common ratio 1/3. Plug the numbers into the formula.
(b) I will assume the third term is supposed to be 2/5^3 instead of 2/5^2....
It's probably easiest to group the terms in pairs. Then the first term is
Grouping the terms in pairs like that then makes the common ratio between the paired terms 1/5^2 = 1/25.
There are the first term and common ratio. Again plug them into the formula.
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