Question

The sum of integers from 1 to 100 that are divisible by 2or 3

Answer 1

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

b) Integers divisible by 3 are - 3,6,9,12,15....99

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)
we must not conaider 6,12,18,24....96o
so b reduces to 3,9,15,21....=3(1+3+5+7+9...33)
use ap formula now and find b ,then add a and b

Answer 2

The intergers from 1 to 100 that are divisible by 2 can be listed as follows:
2×1 , 2×2 , 2×3 ,2×4 , ……. , 2×50.

The sum of these integers is =2×1+2×2+2×3+2×4+….…+2×50

=2(1+2+3+4+…….+50)

=2×50×51/2 (the sum of first 50 natural numbers)

=2550
The intergers from 1 to 100 that are divisible by 3 can be listed as follows:
3×1 , 3×2 , 3×3 ,3×4 , ……. , 3×33.

The sum of these integers is =3×1+3×2+3×3+3×4+….…+3×33

=3(1+2+3+4+…….+33)

=3×33×34/2

=1683