Question

find the sum of natural number between 1 and 100 which are not divisible by 5​

Answer 1

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(25x51)

= 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