## Quiz Information

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## Sample Document Text

Name (printed):
Student ID #:
Section # (or TA's:
name and time)
CMSC 250 Quiz #9 Wednesday, Mar. 31, 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 20 minutes to
complete this quiz. You may not use calculators, textbooks or any other aids during this quiz.
1. [15 pnts.]Use regular induction to prove the following inequality.
?n ? Z where n ? 6, 4n < n2 ?7
Base Case:(n = 6)
4(6) = 24
===================
62 ?7 = 36?7 = 29
===================
24 < 29
Inductive Hypothesis:(n = x)
4x < x2 ?7
Inductive Step:(n = x + 1)
Show:
4(x + 1) < (x + 1)2 ?7
Proof:
By the I.H., 4x < x2 ?7
Adding 4 to both sides, 4x + 4 < x2 ?7 + 4
Doing Algebra, 4(x + 1) < x2 ?3
Since we know that 0 < 2x?3 ?x ? Z?2
We can add the 0 to the left and the 2x?3 to the right and get 4(x+1) < x2 ?3+2x?3
Doing Algebra, 4(x + 1) < x2 + 2x + 1?7
after further algrbr...

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