What is the sum of the first 100 odd numbers?

Question

What is the sum of the first 100 odd numbers?

Answer 1

The sum of the odd natural numbers form 1 to 2n - 1 is S(n) = n².

Example:  What is the sum of the integers from 1 to 99?

Solution:

We need to find n first:

We have that 99 = 2n - 1

Therefore, n = 50

Now we can find the sum:

S(n) = 50² = 2500

Hope this helps!

Answer 2

Sum = 1 + 3 + 5 + .... + 197 + 199

Sum = (0+1) + (1+2) + (2+3) + .... + (98+99) + (99+100)

Sum = (0 + 1 + 2 + ... + 98 + 99) + (1 + 2 + 3 + ... + 99 + 100)

= (99 x 100) / 2   +   (100 x 101) / 2

= 4950 + 5050

= 10,000