Question

Using induction, prove the following: i.) If a > -1 and n is a natural number,...

Using induction, prove the following:

i.) If a > -1 and n is a natural number, then (1 + a)^n >= 1 + na

ii.) If a and b are natural numbers, then a + b and ab are also natural

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove by induction that if a and b are natural numbers, then a + b and...
Prove by induction that if a and b are natural numbers, then a + b and ab are also natural numbers.
Prove by induction. a ) If a, n ∈ N and a∣n then a ≤ n....
Prove by induction. a ) If a, n ∈ N and a∣n then a ≤ n. b) For any n ∈ N and any set S = {p1, . . . , pn} of prime numbers, there is a prime number which is not in S. c) Prove using strong induction that every natural number n > 1 is divisible by a prime.
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive...
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive integersn, 1^3+3^3+5^3+···+(2^n−1)^3=n^2(2n^2−1) (c) For all positive natural numbers n,5/4·8^n+3^(3n−1) is divisible by 19
Prove by induction that if n is an odd natural number, then 7n+1 is divisible by...
Prove by induction that if n is an odd natural number, then 7n+1 is divisible by 8.
Using the method of induction proof, prove: If m and n are natural numbers, then so...
Using the method of induction proof, prove: If m and n are natural numbers, then so are n + m and nm.
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}|...
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}| then n=m
State the Division Algorithm for Natural number and prove it using induction
State the Division Algorithm for Natural number and prove it using induction
Using field axioms and order axioms prove the following theorems (i) The sets R (real numbers),...
Using field axioms and order axioms prove the following theorems (i) The sets R (real numbers), P (positive numbers) and [1, infinity) are all inductive (ii) N (set of natural numbers) is inductive. In particular, 1 is a natural number (iii) If n is a natural number, then n >= 1 (iv) (The induction principle). If M is a subset of N (set of natural numbers) then M = N The following definitions are given: A subset S of R...
How would you prove that for every natural number n, the product of any n odd...
How would you prove that for every natural number n, the product of any n odd numbers is odd, using mathematical induction?
Prove by induction on n that 13 | 2^4n+2 + 3^n+2 for all natural numbers n.
Prove by induction on n that 13 | 2^4n+2 + 3^n+2 for all natural numbers n.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT