Find the sum of odd numbers from 1 to 2001. - Vidyadip

Question

Find the sum of odd numbers from 1 to 2001.

✓

Answer

To find the number of terms in $1+3+5+\ldots \ldots$. 2001,
\[
\begin{aligned}
a_n & =a+(n-1) d \\
2001 & =1+(n-1) \times 2 \\
\Rightarrow \quad \frac{2000}{2} & =(n-1) \Rightarrow n=1001
\end{aligned}
\]
We know that sum of $n$ odd numbers is $n^2$.
$\therefore$ Sum of 1001 odd numbers $=(1001)^2$

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