IIT JEE past question AP GP 6

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S1, S2.... be squares such that for each n>=1, the length of the side of Sn equals to the length of the diagonal of Sn+1...

If side of S1 is 10 cm, for which of these values of n is the area of Sn less than 1 sq. cm?

#Mathematics #Algebra

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Lokesh Verma ·2009-03-26 21:10:57

finish this also.. it is easy

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Asish Mahapatra ·2009-03-26 22:17:25

Let side of S1 = a ... area of S1 = a²
diag of S2 = a ==> side of S2 = a/âˆš2 ... area of S2 = a²/2
diag of S3 = a/âˆš2 ==> side of S3 = a/2 ... area of S3 = a²/4
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Area of Sn = a²/2^n-1

now a = 10cm

So, 100/2^n-1 < 1
==> 2^n-1 > 100
==> n-1 > 7
==> n>8

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IIT JEE past question AP GP 6

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