Proving 6 Statements Using Mathematical Induction - Logic

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This video is about Mathematical Induction; a mathematical proof technique.
The video contains 6 exercises for which statements have to be proved using mathematical induction. We solve the exercises together, so this is a great opportunity for you to practice with (difficult) induction exercises.

The six exercises involve the following concepts:
- The product of a sequence.
- Divisibility.
- Odd and even numbers.
- Recursive definitions (Fibonacci).

We solve the following six exercises:
1. For all n in the natural numbers, except for 1: the product of the sequence from i=2 to n over 1 - 1/(i)^2 = (n+1)/2n.
2. For all n in the natural numbers: 7 divides 8^n -1.
3. For all n in the natural numbers: 11 divides 10^(2n-1) + 1.
4. For all n in the natural numbers: the nth odd number m: 8 divides m^2 - 1.
5. Define dn to be 2 (n=1) or dn-1/2 (n greater than or equal to 2). For all n in the natural numbers: dn = 2/n! (factorial).
6. For all n in the natural numbers: the sum from i=1 to n over F2i-1 = F2n. Where F represents a Fibonacci number.

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This video has been published by MisterCode.

[liamhoward]

Can I suggest to not only read he proofs but to explain the steps of induction.