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Evaluate \huge \frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-.....\frac{1}{2-1/2}}}}}}
We have 100 2's
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7 Answers
62Yagya..
This is not uptil infinity...
and this is for class IX .. (If you have ur answer.. please hide it :P)
1solving the 100th denominator, we get 2-(3/2) as the 99th denominator
solving which we get 2-(1/2) again as the 98th denominator
so 1st denominator will be 3/2
hence on solving we will get 2/3
62Fibonacci...
There is a small thing you have missed out...
Try to think this a bit more..
first step is correct..
36Sir. Here's the solution.....
We get the 99th denominator to be 3/2
So the 98th denominator is 2 - 1/(3/2) = 2 - 2/3 = 4/3
Similarly, 97th denominator is 2 - 1/(4/3) = 2 - 3/4 = 5/4
....................................
We get a series.....
3/2, 4/3, 5/4,.................... to 99 terms..
So the numerator of the above series is 3,4,5,................ to 99 terms = 3 + 98 x 1 = 101
Aand the denominator of the above series is 2,3,4,............... to 99 terms = 2 + 98 x 1 = 100
Hence, the value of the above series is 1/(101/100) = 100/101 Ans....
@Fibonacci sir : Thanks for ur concept..