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...

Algebra ->  Sequences-and-series -> 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...      Log On


   

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) About Me  (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

a%2F%281-r%29

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

2%2F5+%2B+3%2F5%5E2+=+%2810%2B3%29%2F5%5E2+=+13%2F25

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.