Question

what is the formula for the product of first n odd natural numbers​

Answer 1

Step-by-step explanation:

The idea is to "complete the factorials":

1⋅3⋅5⋯(2n−1)=1⋅2⋅3⋅4⋯(2n−1)⋅(2n)2⋅4⋅6⋯(2n)

Now take out the factor of 2 from each term in the denominator:

=(2n)!2n(1⋅2⋅3⋯n)=(2n)!2nn!

A mathematician may object that there is a small gray area about what exactly happens between those ellipses, so for a completely rigorous proof one would take my post and incorporate it into a proof by induction.

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Answer 2

Answer:

n square is the correct answer