What is the sum of all odd numbers between 40 and 100?

Explanation

1. 01

   The odd numbers run 41, 43, …, 99.

2. 02

   Number of terms = $\frac{99 - 41}{2} + 1 = 30$.

3. 03

   Sum = number of terms × average of first and last = $30 \times \frac{41 + 99}{2} = 30 \times 70 = 2{,}100$.