Math Contest #24 [2 SBI]


Here you can keep your brain fit by solving math related problems and also earn SBI or sometimes other rewards by doing so.
The problems usually contain a mathematical equation that in my opinion is fun to solve or has an interesting solution.
I will also only choose problems that can be solved without additional tools(at least not if you can calculate basic stuff in your head), so don't grab your calculator, you won't need it.
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Rules

No upvote, No resteem, No follow required!

I will give the SBI(s) randomly to any participants.

You have 4 days to solve it.

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Problem

Find the limit of the following infinite sum:
Screenshot from 2019-11-23 22-18-40.png

You are allowed to assume convergence because it would be easy to show.

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To everyone who already participated in a past contest, come back today and try a new problem(tell me if you don't want to be tagged):
@addax @ajayyy @athunderstruck @bwar @contrabourdon @crokkon @fullcoverbetting @golddeck @heraclio @hokkaido @iampolite @kaeserotor @masoom @mmunited @mobi72 @mytechtrail @ninahaskin @onecent @rxhector @sidekickmatt @sparkesy43 @syalla @tonimontana @vote-transfer @zuerich

In case no one gets a result(which I doubt), I will give away the prize to anyone who comments.

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@contrabourdon sponsors my contests with 2 STEEM weekly.
You can support him by using a witness vote on untersatz, so he can further support this and other contests.


Comments 5


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24.11.2019 05:54
0
>>> sum([1/(x*(x + 3)) for x in range(1, int(1e8))])
0.611111100938577

But since this is the math contest I assume you're not looking for a numerical solution here?

24.11.2019 10:10
2

No.
This is not only because this is a math contest, but also because your result is not 100% exact.

24.11.2019 11:10
0

I would say you split 1/(x(x+3))=1/(3x)-1/(3(x+3))=1/3(1/x-1/(x+3)). Now if you sum over these terms everything cancels out except 1/3*(1/1+1/2+1/3)=11/18

24.11.2019 10:52
1

Too difficult. I'm out ;-)

26.11.2019 09:36
2