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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