Question

Find the sum of first 1000 positive integers.

Activity :- Let 1 + 2 + 3 + ........ + 1000

Using formula for the sum of first n terms of an A.P.,

S_n = `square`

S₁₀₀₀ = `square/2 (1 + 1000)`

= 500 × 1001

= `square`

Therefore, Sum of the first 1000 positive integer is `square`

Answer 1

Let 1 + 2 + 3 + ........ + 1000

Using formula for the sum of first n terms of an A.P.,

S_n = \[\boxed{\frac{n}{2} (t_1 + t_n)}\]

S₁₀₀₀ = \[\frac{\boxed{1000}}{2} (1 + 1000)\]

= 500 × 1001

= \[\boxed{500500}\]

Therefore, Sum of the first 1000 positive integer is \[\boxed{500500}\].