Find the sum of odd integers from 1 to 2001.

Question

Philoid · Accepted Answer

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

This sequence forms a Arithmetic Progression

Let the first term be ‘a’ and common difference ‘d’.

Let n be the total number of terms in the series.

Here, first term, a = 1

Common difference, d = 2

If l denotes the last term of the series

Then, l = a + (n – 1) × d

Here, l = 2001

⇒ 2001 = 1 + (n – 1) × 2

⇒ 2001 – 1 = (n – 1) × 2

⇒ 2000/2 = n – 1

⇒ 1000 + 1 = n

∴ n = 1001

Sum of A.P. =

⇒ S_n = 1002001

∴ The sum of odd numbers from 1 to 2001 is 1002001.