$$A=\cfrac 6 {\cfrac 6 {\cfrac 6 {6-\cdots}-5}-5}-5 :A=\text{?}$$ my try :
But I want to recurrence Sequence method!!
$$a_{n+1}=\frac{6}{a_n}-5: a_1=\text{?}$$
$$a_2=\frac 6 {a_1}-5,$$
$$a_3=\frac{6}{a_2}-5$$
???
thank you very much !
$A=\frac{6}{\frac{6}{\frac{6}{6-\cdots}-5}-5}-5 :A=\text{?}$
1
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sequences-and-series
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3Try the recursion $a_{n+1} = \frac{6}{a_n} - 5$ – 2017-01-18
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0@Winther. Continuation?!! – 2017-01-18
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0You could try to show that it converges for some suitable initial value(s) $a_0$? – 2017-01-18
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0@Winther. a_1 = ? – 2017-01-18
1 Answers
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$A=\dfrac{6}{A}-5\\A^2=6-5A\\A^2+5A-6=0\\(A-1)(A+6)=0\\A=1\text{ or }-6$