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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