UPSKILL MATH PLUS

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Learn moreThe 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 ${S}_{n}=\frac{n}{2}[a+l]$.

Now, substitute the given values in \(S_n\).

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

${S}_{n}=\frac{n}{2}\times 2n$

\(S_n = n^2\)

**Therefore**, \(S_n = n^2\).

Sum of first \(n\) odd natural numbers \(= n^2\).