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ironjusty
@ironjusty
June 2021
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Bonjour j'ai un petit problème, j'ai une fraction mais je ne sais pas si on peut la simplifier encore:
[tex]\frac{-1-2*[-\frac{1}{2} *(\frac{1}{4})^{n} ]}{-\frac{1}{2} *(\frac{1}{4})^{n} -1} [/tex]
Merci d'avance <3
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ProfdeMaths1
Verified answer
U(n)=(-1-2(-1/2(1/4)^n))/(-1/2(1/4)^n-1)
=(-1+(1/4)^n)/(-1/2(1/4)^n-1)
=(2-2(1/4)^n)/(2+(1/4)^n)
or lim((1/4)^n,n→+∞)=0
donc
lim
(u(n),n→+∞)=2/2=
1
1 votes
Thanks 1
ironjusty
Ah bah merci beaucoup je ne sais pas comment vous avez fait pour savoir que je dois déterminer la limite après mais merci beaucoup :D
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Verified answer
U(n)=(-1-2(-1/2(1/4)^n))/(-1/2(1/4)^n-1)=(-1+(1/4)^n)/(-1/2(1/4)^n-1)
=(2-2(1/4)^n)/(2+(1/4)^n)
or lim((1/4)^n,n→+∞)=0
donc lim(u(n),n→+∞)=2/2=1