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Mathematics-Online course: Basic Mathematics - Natural Numbers | ||

## Mathematical Induction |

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Statements with natural numbers as their parameters can be proved by the Principle of Mathematical Induction. If is a statement that depends on , the method of proof consists of the following two steps:

- Base step (also referred to as initial step): Verify that is true.
- Conclusion (also referred to as inductive step):
Show that the assumption
,, is true``
(induction hypothesis)
implies the truth of , i.e.

The Principle of Mathematical Induction successively infers the truth of a statement from the previous statement . Therefore, if in the base step is verfied for some rather than , then the statement has only been proved for .

(Authors: Kimmerle/Abele)

The formula for the sum of square numbers,

Base step ():

Conclusion (
:

As indicated, the induction hypothesis has been applied to obtain the third equality.

(Authors: Kimmerle/Abele)

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automatically generated 10/31/2008 |