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4. Sequences+Induction

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

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8/27/09 11 MATH 224 – Discrete Mathematics 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. = 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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8/27/09 22 MATH 224 – Discrete Mathematics Basic Properties of Sums = Obj106 From this equality it follows that = = n i nb b 1 = + + = n j n n n j 1 2 6 / ) 1 2 )( 1 (
8/27/09 33 MATH 224 – Discrete Mathematics Proof without Using Induction

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

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