hw3-1 - ES 231322 Discrete Strum fer Cemputer Seienee...

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Unformatted text preview: ES 231322 Discrete Strum fer Cemputer Seienee Heme-work 3 Due Dates: Apt-ll Tm}!!! Q1] Us: the Prieeiple flf Mediematienl [eduefinn te prev: flint 2L1 {Bk-+3] - Hte+ difet‘ an mg 1. {11] Use mlthmeefical inductieutepmve that (a + 3}! teeven fer alipesitive integers n. Q3] Unmathnnatieal induefieu tn prove that Fit - in is divisible hyi fer ail mmmgativeintegen n. Q4) By using maihemetieal inductien, shew that 1*2+2*3+3*4+...+n*[n+1}= .m{n+l{fl;2] Q5] 33 using maihematie-el iJtti.1.It'-tit'lltl.r shew flint: 1+5+53+53+—-+5"—J:J——Lfc-ra11 nan. Q5} fii‘tl’fllt'flfllfih'fl'liflfiflfiflfl efmcfiailuwing: a} a,=4n-2 mheren=l,2,3,... h} a_=]+{-—]]' where ”1.2.3.... e} afl=n{n+l] WELLS," d} Elfin: wheren=l,2,3.... e} 3.131}. the sum efthe integer In and the “WW: integer n. f} ELI") . the [minded effl'te integer m and the nemegefive integfi' e. QT} Use 3mm indueflttn te shew that HT). the numb: efleet'ee efa full binary tree E is I mere than tfl'}. the :11"an ef'inteme] vertiees ef 1‘". WA. minflipped l-titimtewhm: each flip-:emeeepeitherheadeertaile. Hewnuny Feasible nutmmes a] are mere ie tetal? b] mntnin exactly hm heads? e] eel-thin at must thin: tails? d} eeeteiu the same number efheads and mile? Q91Hew may positive integers Ins than men a] tee divisible by T? h} Imditim'blehy?hutnetll? 1:]: mediviaiblcby'ifmdll? d} uedivisiblebyeifl'JerTDrll'? e} mfiifieiblebyneeflyeneefTendH? f] uedifisiblchyneither?ner11? g} havedistieet digits? 11} have distinct digits meiamevm? ...
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