Solve fractions multiplicationI believe this is a very simple one, but I simply can't figure it out. How to solve? 1 2 ⋅ 3 4 ⋅ 5 6 ⋯ 17 18 ⋅ 19 20

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Solve fractions multiplicationI believe this is a very simple one, but I simply can&#039;t figure it out. How to solve?      1    2    ⋅      3    4    ⋅      5    6    ⋯      17    18    ⋅      19    20

Arianna Turner · Accepted Answer

The general compact writing of this sort of fraction is            1      ⋅      3      ⋅      5      ⋯      (      2      n      −      1      )              2      ⋅      4      ⋅      6      ⋯      2      n        =            (      2      n      )      !              (      2      ⋅      4      ⋅      6      ⋯      2      n              )        2              =            (      2      n      )      !                      2                  2          n                    (      n      !              )        2              =      1          2              2        n                                (                            2        n            n                      )              .

Waylon Ruiz · Accepted Answer

Bernard gave the compact formula      A    n    =            1      ⋅      3      ⋅      5      ⋯      (      2      n      −      1      )              2      ⋅      4      ⋅      6      ⋯      2      n        =            (      2      n      )      !                      2                  2          n                    (      n      !              )        2            Now, let me assume that you have large values of   n and that you need a shortcut approximation of the result in a decimal form.The factorial can be evaluated using Stirling approximation  p  !  ≈      2        π        p                (            p    e                      )              n  Applying it to       A    n   gives      A    n    ≈      1          π      n      Applied to   n  =  10 as in your post, this will give a value of   0.178412 while the true value would be   0.176197 which is not too bad (I hope). If you want something better, take an extra term in Stirling formula to get      A    n    ≈      1          π      n                  (        1  −      1          8      n                  )      which would give   0.176182

Solve fractions multiplication I believe this is a very simple one, but I simply can't figure it ou

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