find the sum of all natural numbers amongst first

Question

Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5

Ans:    Sum of all natural numbers in first 1000 integers which are not divisible by 2 i.e. sum of odd integers.

1 + 3 + 5 + .......... + 999

n = 500

S₅₀₀ = 500/2 [1 + 999]

= 2,50,000

No's which are divisible by 5

5 + 15 + 25 ........ + 995

n = 100

Sn = 100/2 [5 + 995]

= 50 x 1000 = 50000

∴ Required sum = 250000 - 50,000

= 200000