Write the sum of first n odd natural numbers. - Vidyadip

Question

Write the sum of first n odd natural numbers.

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Answer

We have,
1 + 3 + 5 + ... up to n terms
$\therefore\text{S}_\text{n}=\frac{\text{n}}{2}[2\times1+(\text{n}-1)\times2]$
$=\frac{\text{n}}{2}[2+2\text{n}-2]$
$=\frac{\text{n}}{2}\times2\text{n}$
$=\text{n}^2$
$\therefore1+3+5+\ ...$ up to n terms = n²
Hence, sum of first n odd natural numbers is n².

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