SOLUTION: For the geometric series 1 - 2/3 + 4/9 - 8/27 ... , find S 8

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Question 1185788: For the geometric series 1 - 2/3 + 4/9 - 8/27 ... , find S 8
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the standard formula for the sum of n first terms of a geometric progression


    S%5Bn%5D = a%2A%28%28r%5En-1%29%2F%28r-1%29%29,


where "a" is the first term, r is the common ratio.


In your case,  n = 8, a = 1, r = -2%2F3.


So,  S%5B8%5D = 1%2A%28%28-2%2F3%29%5E8-1%29%2F%28-2%2F3-1%29%29 = %28%282%5E8%2F3%5E8-1%29%2F%28-5%2F3%29%29 = %282%5E8+-+3%5E8%29%2F%283%5E8%2A%28-5%2F3%29%29 = 

                = %283%2F5%29%2A%28%283%5E8-2%5E8%29%2F3%5E8%29 = %281%2F5%29%2A%28%283%5E8-2%5E8%29%2F3%5E7%29 = 6305%2F%285%2A3%5E7%29 = 1261%2F3%5E7 = 0.5766  (rounded).   ANSWER

Solved.

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On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.