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Question Number 6895 by Chheang Chantria last updated on 02/Aug/16

Commented by Chheang Chantria last updated on 02/Aug/16

help me excercise “ d”

$$\mathrm{help}\:\mathrm{me}\:\mathrm{excercise}\:``\:\mathrm{d}'' \\ $$

Answered by sou1618 last updated on 02/Aug/16

D=Σ_(k=0) ^n (−1)^k C(n,k)2^(n−k) 3^k   D=Σ_(k=0) ^n C(n,k)2^(n−k) (−3)^k   D=(2−3)^n   D=(−1)^n

$${D}=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} {C}\left({n},{k}\right)\mathrm{2}^{{n}−{k}} \mathrm{3}^{{k}} \\ $$$${D}=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}\left({n},{k}\right)\mathrm{2}^{{n}−{k}} \left(−\mathrm{3}\right)^{{k}} \\ $$$${D}=\left(\mathrm{2}−\mathrm{3}\right)^{{n}} \\ $$$${D}=\left(−\mathrm{1}\right)^{{n}} \\ $$

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