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Problem Set 1.2
#2-Induction Proof Case k=1 – Left side:Right side: Induction step: assume true for k. For k+1, – Left side: – Using – assumption: – This is the desired right side.
#2 - continued Aside – note you used this in Calculus to study when a geometric series converges and, if so, what it converges to. That is, if r<1, then the series converges to:
#3- Induction using 2 nd Principle For k=1, both sides are Assume true for all naturals 1,2,3, … k For case k+1, left side (using hint): Note the use of the assumption for k and k-1
#6 - Induction Check for k=4, left side is 24, right side is 16. Assume true for case k, then for case k+1, left: by our assumption To get to the right, use So
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Solved problems on comparison theorem for series.
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……+(4n-3) = n(2n-1) P 1 = 1(2(1)-1)=1 check.
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12-3 Infinite Sequences and Series. Hints to solve limits: 1)Rewrite fraction as sum of multiple fractions Hint: anytime you have a number on top,
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1 Section 3.3 Mathematical Induction. 2 Technique used extensively to prove results about large variety of discrete objects Can only be used to prove.
Copyright © 2007 Pearson Education, Inc. Slide 8-1.
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