# Quiz for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

## Quiz Information

 Material Type: Quiz 8 Professor: Plane Class: CMSC 250 - Discrete Structures Subject: Computer Science University: University of Maryland Term: -- Keywords: Square BracketsCmsc 250 QuizProvided ThatInfinite SetsSubstitutingCombinationsCalculatorsTotal NumberPropositionalYou Have...

## Sample Document Text

CMSC 250 Quiz #8 ANSWERS Wed., Mar. 17, 2004 Write all answers legibly in the space provided. The number of points possible for each question is indicated in square brackets - the total number of points on the quiz is 30, and you will have exactly 15 minutes to complete this quiz. You may not use calculators, textbooks or any other aids during this quiz. 1. [12 pnts.] Write each of the following using summation or product notation: a. 3 + 12 + 27 + 48 + 75 answer =summationtext5i=1(3? i2) b. 12 + 13 + 14 +···+ 1n answer =summationtextni=2(1i) c. 2n × 3n ×···× nn answer =producttextni=2( in) 2. [8 pnts.] Expand the following: a. summationtext6i=3 ii+1 answer = 34 + 45 + 56 + 67 b. producttext5i=2(i2) answer = 22 ×32 ×42 ×52 3. [10 pnts.] Use induction to prove the following. Make sure you clearly specify each step in the appropriate area. The statement to be proved is that nsummationdisplay i=1 (2?3i?1) = 3n ?1 Base Case:(n = 1)summationtext 1 i=1(2?3i?1) by substituting a 1 for every n ...

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