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The radius of the first circle is 1 cm, that of the second is 1/2 cm and that of the third is 1/4 cm and so on indefinitely. The sum of the areas of the circles is ?

Mathematics
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\[\pi + {\pi \over 4} + {\pi \over 16}\cdots\]
Hmm...
You mean to say like this : \[\large{S = \pi + \frac{\pi }{4} + \frac{\pi}{16} + .... }\]

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Other answers:

But what next?
I think it's approaching something.
Well i think we can take : infinite geometric progression ...
pi ( 1 + 1/4 + 1/16 + .... )
Where did you get this question?
http://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%C2%B7_%C2%B7_%C2%B7
I have a book, Math IQ Challenge
It'd be \(\dfrac{4}{3}\pi\)
lol - we solved it before asking it on M.SE :)
:) \[\large{ S _\infty = \frac{a}{1-r}}\] -- infinite geometric series a = 1 r = 1/4 1 / ( 1- 1/4 ) = 1/ (3/4) = 4/3
Yeah ... thanks @ParthKohli

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