### Theory:

The odd natural numbers are $$1$$, $$3$$, $$5$$, ….

We need to find the value of $$1 + 3 + 5 + … + (2n - 1)$$.

First term, $$a = 1$$.

Common difference, $$d = 3 - 1 = 2$$.

Last term, $$l = 2n - 1$$.

This series is an $$A.P$$.
If the first term $$a$$, and the last term $$l$$ are given, then ${S}_{n}=\frac{n}{2}\left[a+l\right]$.
Now, substitute the given values in $$S_n$$.

${S}_{n}=\frac{n}{2}\left[1+2n-1\right]$

${S}_{n}=\frac{n}{2}×2n$

$$S_n = n^2$$

Therefore, $$S_n = n^2$$.
Sum of first $$n$$ odd natural numbers $$= n^2$$.