SOLUTION: Find the sum, if it exists. 32+16+8+...

Question 1033525: Find the sum, if it exists.
32+16+8+...

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is a geometric sequence with common ratio r = 16/32 = 1/2 = 0.5
Take note that 8/16 = 1/2 = 0.5
You can take any term, but the first term, and divide it by its previous term. This will yield the common ratio.

The first term is a = 32.

The infinite sum S is equal to...

S = a/(1-r)

S = 32/(1-0.5) Plug in a = 32 and r = 0.5

S = 32/(0.5)

S = 64

So if you were to add up 32, 16, 8, ... and so on (going on forever following the same pattern), then the sum would be 64.

Final Answer: 64
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