Prove using deductive reasoning the followirg conjectures. If the conjecture is FALSE, give a counterexample.

1. Prove that the negative of any even integer is even

Use the function nest to evaluate p(x) = 1 + x + · · · + x50 at x = 1.00001. (use the matlab ones command to save typing.) find the error of the computation by comparing with the equivalent expression q(x) = (x51 − 1)/(x − 1).

If a and −a are numbers on the number line, which expression must give the distance between them? a) 0 b) a c) |2a| d) |a|

The sum of 5consecutive even numbers is 100. what is the first number in this sequence?