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cse_20_quiz4_solutions

# cse_20_quiz4_solutions - o‘0?4 bk> 4 H-k CSE 20 Summer...

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Unformatted text preview: o‘0}?4 +bk> 4- H-k 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. [351-2 1. '3. n-4=L1.l-2 = Lil-v 911:4 “:5". L%J'2¢LQ51'Z= 2'1" 4 “so: '12-}? —.- L'U-Z" 3'2— : L. 2 L0» 4‘3 «Feel-er out J— - «Ase fur-m l. s . em; .1. WE): 454L=2313= 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 Malawian-3 8:19: Cue '- (slam "Ear- “=03 Lela-‘5' > ‘/' 0 O Ayn-4(o')=0 5 Emmett. Ego-thesis! S‘l’fwm 19k?4\< 4F» Sow. ihl‘eaker L70. T73 tv show -' bm’ 40043 - CL un- deﬁnition) lakH— 4“("El’kltavhrl ‘3) 561m __ 5 (it-bk (L93 cu. LS ﬁ‘hghbh‘) t la unn- ka>4Ck¥D'w\/udn 15 med—wn; +0 238:?” CigM34 +0 CW 5346 070 [mint-fan 1‘” we) ...
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