Question

Find the sum of odd integers from 1 to 2001.

Answer 1

The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.

This sequence forms an A.P.

Here, first term, a = 1

Common difference, d = 2

Here,

a+(n−1)d = 2001

=> 1+(n−1)(2) = 2001

=> 2n−2 = 2000

=> n = 1001

Sn = n/2[2a+(n−1)d]

∴ Sn = 1001/2[2×1+(1001−1)×2]

=1001/2[2+1000×2]

=1001/2×2002

=1001×1001

=1002001

Hence, the sum of odd numbers from 1 to 2001 is 1002001.