Find a formula for when m is a positive integer.There is also a special notation for products. The product of is represented by read as the product from j = m to j = n of a j.

Solution:Step-1: In this problem we need to find the formula for ,where m is a positive integer.NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing. Example : Step-2: ........(1). Step-3:Observe the above summation value : 1 occurs at 7 times , 2 occurs at 19 times , 3 occurs at 7 37 times and so on.So, the numbers 1 , 2, 3….. are occurs at ( 7 , 19 , 37…..times).By mathematical...