Question

Find the sum of odd numbers from 1 to 2000.

Answer 1

1000000

Explanation:

Finding the sum of first 'n' odd numbers:

1 to 2000.

Here, We don't know how many odd numbers are there. We can find the number of odd numbers using the below formula,

`\boxed{a_n = a + (n-1)*d}`

1,3,5,.........1999

aₙ = 1999 ; a = first term = 1

Common difference = d = 2

1 + (n -1)* 2 = 1999

Subtract 1 from both sides,

(n -1) *2 = 1999 -1

(n -1)*2 = 1998

Divide both sides by 2,

n - 1 = 1998 ÷ 2

n - 1 = 999

Add 1 to both sides,

n = 999 + 1

n = 1000

`\boxed{\text{\bf Sum of first 'n' add numbers = $\bf n^2$}}`

= 1000 * 1000

= 1000000