Find the sum of odd integers from 1 to 2001.
The odd integers from1 to 2001 are 1,3,5,...1999,2001.
This sequence form an A.P.
Here, first term is, a=1 and common difference, d=2
Here a+(n−1)d=2001
⇒1+(n−1)(2)=2001
⇒2n−2=2000
⇒n=1001
Hence required sum is,
Sn=n2[2a+(n−1)d]
=10012[2×1+(1001−1)×2]
=10012[2+1000×2]
=10012×2002
=1001×1001
=1002001