Consider the program fragment below:

Integer j, k

Sum 0

For k = 1 to n do

J = n

While j>1 do

Sum = sum + j

J = j/2

End-while

End-for

Derive a formula for the number of repetitions of the while loop.

Derive a formula for the value of sum computed by the while loop.

Derive the formula for the value of sum computed by the whole program fragment.