Question

Find the sum of all natural numbers from 31 to 60.
Hint: Sum of first 10 natural numbers is 55.

Answer 1

Sum of numbers from 1 to 10 = 55

Sum of numbers from 31 to 60 = Sum of numbers from 31 to 40 + Sum of numbers from 41 to 50 + Sum of numbers from 51 to 60


Sum of numbers from 31 to 40 =
31 + 32 + 33 + ..... + 39 + 40

It can be written as
(30 + 1) + (30 + 2) + ..... + (30 + 10)
= (30 x 10) + (1 + 2 +3 + ... + 10)
= 300 + 55
= 355

Similarly, sum of numbers from 41 to 50 = (40 x 10) + 55
= 455

And, sum of numbers from 51 to 60 = (50 x 10) + 55
= 555

Thus, sum of numbers from 31 to 60 = 355 + 455 + 555 = 1365