Question 41545: Find the sum of the following series:
1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...
I tried to use the sume of an infinite series formula, but there is no common ratio. I also tried seeing if some of the terms will cancel or add up to the same thing, but I am still not getting anywhere.
Answer by mszlmb(115)   (Show Source):
You can put this solution on YOUR website! 1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...
excuse me as you'll have to post
"Find the sum of the following series:
1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...
I tried to use the sume of an infinite series formula, but there is no common
ratio. I also tried seeing if some of the terms will cancel or add
up to the same thing, but I am still not getting anywhere."
again, but do the numbers have a pattern at all?
1+1/2+1/3+1/4+1/9+1/8+1/27+1/16...?
Do you mean 1+1/2+1/3...?
Hey I found it!
it's 1/1+1/2+1/3+1/4+1/9+1/8
you see, 4 is 2*2, 8 is 4*2, 9 is 3*3, get it?
it's the sum of two infinite series:
1/3+1/9+1/27 etc..
AND 1/1+1/2+1/4+1/8...
1/1+1/2+1/3+1/4+1/9+1/8+1/27+1/16...
COOL! so now just use the formula (which I can't recall) to get each's infinite sum, and add them up!
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