Asked by Venki
The values of 4+(1/4+(1/4+1/4+..upto infinity...
I don't know how to type that fraction .
I have taken a photo and uploaded here.
ibb[dot]co/fLqhxH
Please help me in solving
I don't know how to type that fraction .
I have taken a photo and uploaded here.
ibb[dot]co/fLqhxH
Please help me in solving
Answers
Answered by
Reiny
Your link did not work, but I think you are attempting to write a continued repeating fraction.
Here is a link to introduce you to the topic of continued fractions
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#section1.5
it is clear that its value > 4 , so let x = 1/4 + [1/4 + [ ..... , only the decimal part
notice that we see that pattern repeating in the second level
SOOO, could we not say: ?
x = 1/(4+x) ??
then, 4x + x^2 = 1
x^2 + 4x - 1 = 0
x = (-4 ± √20)/2
= -2 ± √5, but x is clearly positive,
x = √5 - 2
so your repeating continued fraction = <b>2 + √5</b> or appr 4.236068
Here is a link to introduce you to the topic of continued fractions
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#section1.5
it is clear that its value > 4 , so let x = 1/4 + [1/4 + [ ..... , only the decimal part
notice that we see that pattern repeating in the second level
SOOO, could we not say: ?
x = 1/(4+x) ??
then, 4x + x^2 = 1
x^2 + 4x - 1 = 0
x = (-4 ± √20)/2
= -2 ± √5, but x is clearly positive,
x = √5 - 2
so your repeating continued fraction = <b>2 + √5</b> or appr 4.236068
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