Question

What is the value of the sum of the first 100 even numbers?

Answer 1

(2 + 4 + 6 +8 + … + 200)

= 2 × (1 + 2 + 3 + 4 + … 100)

= 2 × (1+100 + 2+99 + 3+98 + … + 50+51)

(Just changing the order of the numbers)

= 2 × (101 + 101 + 101 + … + 101)

This gives 50 pairs of numbers, each of which adds up to 101

= 2 × 50 × 101

= 10100