Q

Find the sum of odd integers from 1 to 2001.

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

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Odd integers from 1 to 2001 are $1,3,5,7...........2001.$

This sequence is an A.P.

Here , first term =a =1

common difference = 2.

We know , $a_n = a+(n-1)d$

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

$\Rightarrow \, \, 2000 = (n-1)2$

$\Rightarrow \, \, 1000 = (n-1)$

$\Rightarrow \, \, n=1000+1=1001$

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

$= \frac{1001}{2}[2(1)+(1001-1)2]$

$= \frac{1001}{2}[2002]$

$= 1001\times 1001$

$= 1002001$

The , sum of odd integers from 1 to 2001 is 1002001.

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