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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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