Consider the following program segment, where i, j, k, n, and counter arc integer variable...

Consider the following program segment, where i, j, k, n, and counter arc integer variables and the value of n (a positive integer) is set prior to this segment.

We shall determine, in two different ways, the number of times the statement

counter := counter + 1

is executed. (This is also the value of counter after execution of the program segment.) From the result in Example 1.39, we know that the statement is executed  times. For a fixed value of i, the for loops involving j and k result in  executions of the counter increment statement. Consequently,  Use this result to obtain a summation formula for