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Find the sum of all odd integers from 1 to 1001.

Answer» The odd integers from 1 to 1001 are 1,3,5,7,……,999, 1001.
This is an AP in which a=1, d= ( 3-1) = 2 and l = 1001 .
Let the number of terms be n.Then,
` T_(n) 1001 Rightarrow a+ ( n-1) d= 1001`
` Rightarrow 1+ (n-1)xx2 =1001 Rightarrow n = 501`
Now, a=1, l = 1001 and n = 501
`S_(n)=n/2(a+l)=501/2.( 1+1001)=(501xx501) = 251001`

Hence, the required sum is 251001


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