What type of fraction is the following one 1/2/3/4/5/6...............,,,n

Questions
1

Sir
What type of fraction is the following one

1/2/3/4/5/6…,n

1/2/3/4/5/6 = 5/16 = 0.3125 by Wolfram partial decomposition Calculator

By Google Calculator and Microsoft Excel 1/2/3/4/5/6 = 1/720 = 0.00138888888

Please comment on the algorithms involved and advise.

2

Mathematica gives 1/2/3/4/5/6 = 1/720. Partial fractions have a special order of evaluation, from right to left. You must know what you are doing.

3

The partial fraction decomposition calculator has an unusual interpretation of the input. For example 1/x y becomes 1/(x y). It is a design choice that leaves me uneasy.