Unformatted text preview: o‘0}?4 +bk> 4 Hk CSE 20 Summer 2008 Instructor: Cynthia Lee
Quiz4 Name: SYN 141'sz 1. (2 points) Write the ﬁrst ﬁve terms of the sequence deﬁned by this formula: ﬁ,1 = L43] 2 for all integers n 2 “=7 :Lj'i km; g. [3512 1. '3.
n4=L1.l2 = Lilv 911:4
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5' 5L [0 1° 7: 3. (1'1 points) Notes: In proofs you may use any rule of algebra without explicitly naming
the rule, however you should do algebra work one step at a time So all work is shown. You must
identify other theorems and deﬁnitions when you are using them. Also, if you use a. property
you have assumed to be true (hint: tn the inductive step), you should very clearly identify when
this assumption is being invoked. For this quiz, I am. primarily interested in. seeing that you
understand the framework of on induction proof. The majority of points can be earned just by
carefully including each port of the proof, even. if the ‘ﬁm'ddle” ts incomplete. 0n the ﬂip stole,
a correct "middle” that locks key parts of the framework (if such a thing is even possible), will
not get a good grade. A sequence bo.b1,b2. . .. is deﬁned by letting b0 = 5 and bk 2 4 + bhl for all integers k .2 1.
Show that on > 4n for all integers n 2 0. 5L:
“53. Lil’2': L*.l'1=‘l'2"' 5, 2. (2 points) Compute the sum (show your work!): 2 5. A! f], ,’L on Theorem: loh> 4h “Fur all. in‘l’cﬁers V130 CL,“ as deﬁned above) PM? ' (L3 Malawian3
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 Summer '08
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