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Mathematical induction is used in mathematics to prove many
statements, in particular it is used to prove statements, theorems, or even formulas
that are asserted by all natural numbers. When we say “all” natural numbers it
means any natural number that we may possibly come across on. In order to prove
by mathematical induction, we must first go over some very important rules.

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Rules:

1.) If when a statement, theorem, or formula is true for any natural number \(n=k\) then it is also true for \(n=k+1\)

and

2.) The statement is true for \(n=1\) then the statement will be true for every natural number \(n\).

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To prove a statement by induction, the first step that must
be done is to prove part one. According to part one, if this is true then step two is also true. After applying step two we are now implying that the statement
will be true for \(n=2,3,4\), and so on.

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