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Mathematical Induction

Hi readers, I guess this post goes under algebra.  Today, we will be introducing a new method and in case you haven't read the title, it's the INDUCTION METHOD!!! Mathematical induction is a powerful method to prove some mathematical statement for all natural numbers (positive integers). Consider this: Show that

for every natural n.

Now we are going to use mathematical induction to prove this.

Induction has just 2 steps:

1. Basic/Base Step: Show that the statement holds for n = 1
2. Inductive step: Show that the statement holds for n = n + 1
Basically its showing that it works for the first natural number (1) and every subsequent natural number (k+1).

So, we will first prove the basic step, which is n=1. Obviously, when you substitute 1 in the equation, the statement holds. To show that this holds for every natural number n, we use n=n+1.  We get the equation

.

So this proves that the equation hold for n=n+1, and every subsequent value of n.

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