Question

Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.

Answer 1

The natural numbers which are divisible by 2 or 5 are:
2 + 4 + 5 + 6 + 8 + 10 + ... + 100 = (2 + 4 + 6 + ... + 100) + (5 + 15 + 25 + ... + 95) Now respectively.
Therefore,
$2+4+6+\dots \dots +100=2\frac{50}{2}(1+50)$
= 2550
Again
5 + 15 + 25 + ... + 95 = 5(1 + 3 + 5 + ... + 19)
$=5\left(\frac{10}{2}\right)(1+19)$
= 500
Therefore the sum of the numbers divisible by 2 or 5 is:
2 + 4 + 5 + 6 + 8 + 10 + ... + 100 = 2550 + 500
= 3050