Marcos_Kata_Magnet_Particules

[marcos-x86]

Full description image with equations: https://s26.postimg.org/bcoukewll/Marcos_Magnet_particules.jpg

Professor Chambouliard hast just discovered a new type of magnet material. He put particles of this material in a box made of small boxes arranged in K rows and N columns as a kind of 2D matrix K x N where K and N are postive integers. He thinks that his calculations show that the force exerted by the particle in the small box (k, n) is:

[v(k, n) = \frac{1}{k(n+1)^{2k}}]

The total force exerted by the first row with k = 1 is:

[u(1, N) = \sum_{n=1}^{n=N}v(1, n) = \frac{1}{1.2^2} + \frac{1}{1.3^2}+...+\frac{1}{1.(N+1)^2}]

We can go on with k = 2 and then k = 3 etc ... and consider:

[S(K, N) = \sum_{k=1}^{k=K}u(k, N) = \sum_{k=1}^{k=K}(\sum_{n=1}^{n=N}v(k, n)) \rightarrow (doubles(maxk, maxn))]

#Task: To help Professor Chambouliard can we calculate the function doubles that will take as parameter maxk and maxn such that doubles(maxk, maxn) = S(maxk, maxn)? Experiences seems to show that this could be something around 0.7 when maxk and maxn are big enough.

#Examples:

double(1, 3) => 0.4236111111111111
double(1, 10) => 0.5580321939764581
double(10, 100) => 0.6832948559787737

[codecov-io]

Codecov Report

Merging #138 into develop will increase coverage by 0.04%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##             develop     #138      +/-   ##
=============================================
+ Coverage      87.84%   87.89%   +0.04%     
- Complexity       456      459       +3     
=============================================
  Files            103      104       +1     
  Lines            987      991       +4     
  Branches         161      161              
=============================================
+ Hits             867      871       +4     
  Misses           106      106              
  Partials          14       14

Impacted Files	Coverage Δ	Complexity Δ
.../java/org/fundacionjala/coding/marcos/Magnets.java	100% <100%> (ø)	3 <3> (?)

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