Combinations

If the order doesn't matter, in how many ways can the first 100 natural numbers be grouped if we take 2 numbers in one group?

For example, if we have the set of numbers \((a,b,c,d)\), then they can be arranged in the following manner:

\[ \{ ab , bc , cd , ac , bd , ad \} , \]

so, there are 6 ways in which these 4 numbers can be paired in pairs of 2.

Bonus: What could be the general formula for this type of scenario?

Grand Bonus: Find the sum of all the combinations.

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