Here you can keep your brain fit by solving math related problems and also earn [SBI](https://steemit.com/@steembasicincome) 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.
*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*
# Rules
#### No upvote, No resteem, No follow required!
#### I will give the SBI(s) randomly to any participants.
#### I will give 10 STEM to every one who gets the bonus question.
#### You have 4 days to solve it.
*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

# Problem
After the infinite sum last week I want you to do a sequence today:
![Screenshot from 2019-10-26 22-11-59.png](https://cdn.steemitimages.com/DQmaDopsZ4FHfq8dDma9QcHQvAeYs4rZxeYwNBFLY1K5vVT/Screenshot%20from%202019-10-26%2022-11-59.png)

1. Does the sequence converge?
2. If yes what is the limit of the sequence?
3. Bonus(10 STEM if you solve it!): Can you construct a similar sequence that converges to √n, where n is your reputation?

To 3.: 
I ask for your the square root of your reputation here because I want to give everyone the opportunity to get a result by thinking for themselves and not copying from others. So please just enter the result for 3 without any extra comment.

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

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 @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.
 
*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

@contrabourdon sponsors my contests with 2 STEEM weekly.
You can support him by [using a witness vote on untersatz](https://v2.steemconnect.com/sign/account-witness-vote?witness=untersatz&approve=1), so he can further support this and other contests.