Here you can solve interesting problems using whatever programming language you like. Also you will earn SBI and sometimes STEM by doing so.
Also you might learn new things by doing so.
The tasks will be rather hard to solve without a programmable computer and some programming skills, but if you want to add a few million numbers by hand or similar, I would still give you the reward.
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Rules

No upvote, No resteem, No follow required!

I will give 2 SBI for every correct entry.

If two pieces of code are to closely related I might consider the later of them as copied which results in no prize for that person.

You have 4 days to solve it.

Even though this is about computation I will also accept algebraic solutions if you find one.

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Problem

Today I want you to do some numerical stuff.
Consider the following sum:

s is a complex number with
s = 0.5 + yi
The sum does converge for any real y.

Now your task is to use numerical methods to find the smallest value for y > 0 where the sum does converge to 0.

You don't need to be more precise than 3 decimal places.

Tip: The distance between any two consecutive zeros of the sum is generally bigger than 1.

Tip 2(added on @crokkon 's request): There are several 100 zeros between 1 and 1000.

If you don't know complex numbers it would be time to learn about them. They are pretty useful in many cases!

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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):
@crokkon @kaeserotor

In case no one gets a result(which I doubt), I will give away the prize equivalent of one participant to the person who makes the most constructive description why the problem is too hard in your opinion.

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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.