Find the sum of odd integers from 1 to 2001.
Question:

Find the sum of odd integers from 1 to 2001.

Solution:

The odd integers from 1 to 2001 are $1,3,5 \ldots \ldots 2001$.

It is an AP with $a=1$ and $d=2$.

$a_{n}=2001$

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

$\Rightarrow 2 n-2=2000$

$\Rightarrow 2 n=2002$

$\Rightarrow n=1001$

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

$\Rightarrow S_{1001}=\frac{1001}{2}[2 \times 1+(1000) 2]$

$\Rightarrow S_{1001}=\frac{1001}{2} \times 2002=1002001$

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