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## #1 2020-01-13 08:15:02

mrpace
Member
Registered: 2012-08-16
Posts: 83

### Find the limit of this series

What does this series converge to?

16/3 + 32/9 + 16/27 + 32/81 + ......

Any help is appreciated

Thanks

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## #2 2020-01-13 20:08:54

bob bundy
Registered: 2010-06-20
Posts: 8,702

### Re: Find the limit of this series

hi

This is two geometric series put together:

16 x (1/3 + 1/27 + …) + 32 x (1/9 + 1/81 + ...)

The common ratio is r = 1/9 for both.  The start numbers are a = 1/3 and 1/9.

The formula for the sum to infinity of a GP is  a/(1-r)

https://www.mathsisfun.com/algebra/sequ … etric.html

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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