Question

find the sum of the odd integers between 14 to 58​

Answer 1

Answer: Any sum of a sequence of odd numbers starting with 1 is a square.  In particular, the odd numbers running from 1 to 13 total 7^2 and the odd numbers from 1 to 57 total 29^2.  (Note that two 7's minus 1 is 13 and two 29's minus 1 is 57.)  

Subtracting the two gives us that the odds between 14 and 58 total 29^2 - 7^2 = (29 + 7)

Answer 2

Answer:

The sum of odd numbers from 14 to 58 is 792