Induction

Induction - ITI 111 1/28/2011 Lecture 4 notes Mathematical...

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ITI 111 1/28/2011 Lecture 4 notes Mathematical Induction Summation Notation The mathematical notation of infinite sums is often done using “big sigma” notation. The variable that is changing is written beneath the sigma, usually with its starting value. Its ending value is then written above the sigma. Oftentimes, the variable is not repeated on the top, an only the ending value is placed there. If no value is placed at the top, it is assumed to be infinity. So if we have: ± ²³´ ²³µ This can be expanded as: ± · ¸ ± · ¹ ± Or using the formula for the n th odd number, we can calculate the sum of, say the first 5 odds: ∑º» ¼ ½ ¾ ¿º¿½) ¼ ½) · ¿º¿º) ¼ º) · ¿º¿¶) ¼ ½) · ¿º¿¸) ¼ ½) · ¿º¿¹) ¼ ½)À ´ Á³Â = 1 + 3 + 5 + 7 + 9 = 25 Mathematical Induction Mathematical induction is a way of proving series of statements. It is especially useful in set theory, as sets are both discrete (have a elements) and potentially infinite in size. It is often easiest to understand if examined through an example.
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This note was uploaded on 02/20/2012 for the course 790 373 taught by Professor Boros during the Fall '09 term at Rutgers.

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Induction - ITI 111 1/28/2011 Lecture 4 notes Mathematical...

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