Just simple question !

Algebra Level 3

what is the value of the above expression ?

The answer is 2.

2 solutions

Aditya Raut
Jun 3, 2014

Let value of given expression be $x$ . ... (here i mean that $\displaystyle x = 4 - \dfrac{4}{4-\dfrac{4}{4-\dfrac{4}{4-4 } \dots }}$

Then As we have it upto infinity,

$x = 4 - \dfrac{4}{x}$ Hence $x^2-4x+4=0$ And only possibility is $x =\boxed{2}$

I did not see the vertical ellipsis on the image until I saw your answer. Thank you, your answer was illuminating because it made me see that the question was not (as I thought) the finite expression:

"find the value of 4 - 4 / (4 - 4 / (4 - (4/4-4)))",

but rather a question about an infinitely long expression. The fact that the answer box was configured to take a finite integer as the answer tends to confirm that your interpretation of the question was the intended meaning of the questioner.

I do think that your response is correct for the intended question, and that they should think about re-drawing the problem statement image to make the ellipsis more obvious, for example they could add the phrase "and so on" at the bottom of the whiteboard.

P.A. McCaul - 7 years ago

tq for ur comment , i will try improve next time ...

Bleach Byakuya - 7 years ago

i did the same thing....

Jitesh Mittal - 6 years, 10 months ago

what is it???? out of thinking

ali haider - 6 years, 11 months ago

It's more explained , see now ...

Aditya Raut - 6 years, 11 months ago

how do we get 'x' as the denominator of 4?

arjun singh - 6 years, 11 months ago

Because it's an infinite sequence, see that the same thing as $x$ is seen in the denominator if you see it as an infinite thing .... @arjun singh

Aditya Raut - 6 years, 11 months ago

Bleach Byakuya
May 24, 2014

Let the above expression is X , and we will get

X = 4 - 4/X , then just solve it as a simple equation .

Just simple question !

The answer is 2.

2 solutions

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