A proof is nothing more than having sufficient evidence to establish truth.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
In mathematics, that means we must have a sequence of steps or statements that lead to a valid conclusion, such as how we created Geometric 2-Column proofs and how we proved trigonometric Identities by showing a logical progression of steps to show the left-side equaled the right-side.
Well, the Proof by Mathematical Induction, or the Principle of Mathematical Induction, is a way for us to prove a statement is true by first making an assumption or hypothesis.
There are only three steps for a Proof by Mathematical Induction before we can draw our conclusion.
The Principle of Mathematical Induction
This may seem strange at first, but it’s really quite simple. In fact, I love how Math is Fun describes this in a more visual way: Imagine you’ve placed dominos on end, and you let the first domino fall (step 1), well, if the dominos are close to each other, then the next domino will fall too (step 2), and so that means that eventually all the dominos will fall (step 3).
Now, let me just say that the first two steps will be extremely straightforward, with hardly any work to do, but the heart of this proof is found in step 3, where we must show that Step 2 really does lead us to Step 3.
But don’t worry, it’s not hard and again, there are only three steps! Yay!
So, together we will look at five questions in detail and see how to Prove by Mathematical Induction algebraic and series expressions and formulas.
Mathematical Induction – Video
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