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Question Number 138059 by sahnaz last updated on 09/Apr/21

((2^(n+1) + 3^(n+2) + 4^(n+3) )/(2^n +3^n +4^n ))=?

$$\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} +\:\mathrm{3}^{\mathrm{n}+\mathrm{2}} +\:\mathrm{4}^{\mathrm{n}+\mathrm{3}} }{\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} }=? \\ $$

Answered by MJS_new last updated on 10/Apr/21

9+((2^n (55×2^n −7))/(3^n +2^n (2^n +1)))  lim_(n→−∞)  =2  lim_(n→+∞)  =64

$$\mathrm{9}+\frac{\mathrm{2}^{{n}} \left(\mathrm{55}×\mathrm{2}^{{n}} −\mathrm{7}\right)}{\mathrm{3}^{{n}} +\mathrm{2}^{{n}} \left(\mathrm{2}^{{n}} +\mathrm{1}\right)} \\ $$$$\underset{{n}\rightarrow−\infty} {\mathrm{lim}}\:=\mathrm{2} \\ $$$$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:=\mathrm{64} \\ $$

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