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Question-6895




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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