Math Contest #22 Results and Solution

Words
121
Reading
1 min
Listen
Play
7y

Solution

The problem of this contest was to proof euler's function:

This can be done using taylor series at x = 0 because all 3 functions are continuous and have continuous derivatives:
You can see the taylor series as given, but they are on the other hand not too hard to construct because all three functions have cyclical repeating derivatives. And seeing that they are similar isn't that hard then:
Screenshot from 2019-11-14 22-14-30.png

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

List of participants with their entries:

Namesolution foundcomment
crokkon@crokkoncorrect
kaeserotor@kaeserotorcorrect

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

Winner draw:

Not necessary since the reward can be divided be the number of entries:
Congratulations kaeserotor@kaeserotor and crokkon@crokkon , you won 1 SBI each!
↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

The next contest starts in 2 days. Don't miss it!