Find the sum of odd integers from 1 to 2001.

Solution:

The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.

This sequence forms an A.P.

Here, first term, a = 1

Common difference, d = 2

Here, $a+(n-1) d=2001$

$\Rightarrow 1+(n-1)(2)=2001$

$\Rightarrow 2 n-2=2000$

 

$\Rightarrow n=1001$

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$\therefore S_{n}=\frac{1001}{2}[2 \times 1+(1001-1) \times 2]$

$=\frac{1001}{2}[2+1000 \times 2]$

$=\frac{1001}{2} \times 2002$

$=1001 \times 1001$

 

$=1002001$

Thus, the sum of odd numbers from 1 to 2001 is 1002001.