Evaluate:1+2+3+.....+100 in a pattern.

1 + 2 + 3....+ 100

The above is the sum of the first 100 natural numbers

Answer:

1 = 1

1 + 2 = 3

1 + 2 + 3 = 6 = 3(3+1)/2

1 + 2 + 3 + 4 = 10  = 4 (4+1)/2

........

From the above pattern, the formula has been developed as follows

The formula for the sum of the first n natural numbers is

Sn = n(n + 1)/2

So the sum of the first 100 natural numbers, S100 = n(n + 1)/2 = 100(100+1)/2

  = 50 x 101 = 5050

Tutorialspoint

Updated on: 10-Oct-2022

30 Views

Kickstart Your Career

Get certified by completing the course

Get Started