The odd integers from 1 to 2001 are \(1,3,5, \ldots 1999,2001\).
This sequence forms an A.P.
Here, first term, \(a=1\)
Common difference, \(d=2\)
Here,
$$
\begin{aligned}
&a+(n-1) d=2001 \\
&=>1+(n-1)(2)=2001 \\
&\Rightarrow 2 n-2=2000 \\
&\Rightarrow n=1001 \\
&S n=n / 2[2 a+(n-1) d] \\
&\therefore S n=1001 / 2[2 \times 1+(1001-1) \times 2] \\
&=1001 / 2[2+1000 \times 2] \\
&=1001 / 2 \times 2002 \\
&=1001 \times 1001 \\
&=1002001
\end{aligned}
$$
Hence, the sum of odd numbers from 1 to 2001 Is \(1002001 .\)
