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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