Discrete math

(Please Show all steps)

1.Give a proof by contradiction of the following: "If n is an odd integer, then n² is odd."

2.Use the Principle of Mathematical Induction to prove the summation formula. Be sure to identify where you use the inductive hypothesis.

LetP(n) be the statement that 1³+ 2³ + ... +n³=(n(n+ 1)/2)² for the positive integern.

What is the statementP(1)?

Show thatP(1) is true, completing the basis step of the proof.

What is the inductive hypothesis?

What do you need to prove in the inductive step?

Complete the inductive step, identifying where you use the inductive hypothesis.

Explain why these steps show that this formula is true whenevernis a positive integer.