Question

Please help find the sum of all even integers from 2 to 100

Answer 1

2550

Explanation:

2 + 4 + 6 + ……… + 98 + 100

= (2×1) +(2×2) + (2×3) + ……… + (2×50)

= 2 × (1 + 2 + 3 + ………. + 50)

The sum (S) of n natural numbers is given by -

S = (n × (n + 1) )/2

Therefore,

2 × (1 + 2 + 3 + ……… + 50)

= 2 × ((50 × 51)/2)

= 2 × (2550/2)

= 2 × 1275

= 2550

Hope this helps!