2. Sequences+Induction

# 2. Sequences+Induction - MATH 224 Discrete Mathematics...

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1 08/27/09 MATH 224 – Discrete Mathematics = n i i 1 = n j j ar 0 Sequences and Sums A sequence of the form ar 0 , ar 1 , ar 2 , ar 3 , ar 4 , … , ar n , is called a geometric sequence and occurs quite often in computer science applications. Another common sequence is of the form a, 2a, 3a, 4a, … , na is called an arithmetic sequence. We have seen this when examining the number of steps executed by selection sort. In our example a was equal to 1, so we just had 1, 2, 3, … . N. Often we are interested in the sum of one of these sequences as in the arithmetic sum and the geometric sum. 2 ) 1 ( n n + = r r a n - - + 1 ) 1 ( 1 = Arithmetic Sum Geometric Sum (as long as r ≠ 1) What will be the formula for the geometric sum when a = 1. Compare this to the formula on Page 155 from our text. Are they equivalent?

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08/27/09 MATH 224 – Discrete Mathematics = n i ai 1 = n i i a 0 Basic Properties of Sums = + = = = + = n k i n i k i i f i f i f 1 1 1 ) ( ) ( ) ( From this equality it follows that
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## This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Spring '08 term at Southern Illinois University Edwardsville.

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2. Sequences+Induction - MATH 224 Discrete Mathematics...

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