Answer
--Proving The algorithm for computing nx whenever n
is a positive integer and x is an integer, using just addition.
Work Step by Step
--If n = 1,
- then
-nx = x, and the algorithm correctly returns x.
- Assume that the algorithm correctly computes kx. To compute (k + 1)x
-it recursively
- computes the product of k + 1 − 1 = k and x,
and then adds x.
-- By the inductive hypothesis,
-it computes that product correctly, so the answer returned is
kx+x = (k+1)x,
which is correct.