Mathematical Induction

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How to solve a mathematical problem?

-Read carefully and make sure you understand what is being asked.

To make sure you understand:

-What is unknown?

-What are the given quantities?

-What are the given conditions?

-Draw pictures!

Then make a plan towards a solution:

-Recognize something familiar.

-Recognize patterns.

-Use analogies.

-Take simpler cases.

-Reason indirectly.

-Introduce extra conditions, constraints and/or assumptions.

-Establish sub-goals.

-Use mathematical induction.

Mathematical induction:

Sn true?

1. Show that S1 is true. 2. Assume that Sk is true, prove that Sk+1 holds.