What is the inductive hypothesis

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Reference no: EM13854507

1. Prove or disprove.

A. The difference of any two odd integers is odd.

B. An odd integer minus an even integer is odd.

2. Given _(i=1)∑ⁿ [(2i-1)=n²]

A. Write P(n) without using the sigma (∑) notation.

B. Do a proof by mathematical induction using the 4 steps below to show that the statement is true for every positive integer n:

Hint: use the weak principle of mathematical induction.

Show that the base step is true

What is the inductive hypothesis?

What do we have to show?

Proof proper:

3. Do a proof by mathematical induction using the 4 steps below to show that the following statement is true for every positive integer n:

Hint: use the weak principle of mathematical induction.

5+10+15+...+5n =(5n(n+1))/2

Show that the base step is true

What is the inductive hypothesis?

What do we have to show?

Proof proper (Justify each step):

4. Prove using mathematical induction that 2^(3n) - 1 is divisible by 7 for all n ∈N.

a. Show that the base step is true

b. What is the inductive hypothesis?

c. What do we have to show?

d. Proof proper (Justify each step):

Reference no: EM13854507

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