Question

The sum of the integers from 1 to 100 that are divisible by 2 or 5 is

Answer 1

HEY HERE IS YOUR ANSWER...

a) Integers divisible by 2 are - 2,4,6,8,…,100

b) Integers divisible by 5 are - 5,10,15,…,100

summing up (a),

2(1 + 2 + … + 50)

= 2(25 x 51)

= 2550 ………………………………………………….(1)

Now while summing up (b), we must not consider those numbers, we already did in (a)

So, we must not consider 10,20,40, … , 100

So, (b) reduces to - 5,15,25,35,…,95  

summing it up,

=5(1 + 3 + 5 + … + 19)

use Arithmetic Progression, sum formula,  

= 5 x 100 = 500 ………………………………………(2)  

So, answer is (1) + (2) = 3050

HOPE THIS WOULD BE HELPFUL TO YOU...