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 2 years ago
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 ?
 2 years ago
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 ?

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1\[\pi + {\pi \over 4} + {\pi \over 16}\cdots\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1You mean to say like this : \[\large{S = \pi + \frac{\pi }{4} + \frac{\pi}{16} + .... }\]

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1I think it's approaching something.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1Well i think we can take : infinite geometric progression ...

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1pi ( 1 + 1/4 + 1/16 + .... )

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Where did you get this question?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1http://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%C2%B7_%C2%B7_%C2%B7

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1I have a book, Math IQ Challenge

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1It'd be \(\dfrac{4}{3}\pi\)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1lol  we solved it before asking it on M.SE :)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1:) \[\large{ S _\infty = \frac{a}{1r}}\]  infinite geometric series a = 1 r = 1/4 1 / ( 1 1/4 ) = 1/ (3/4) = 4/3

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah ... thanks @ParthKohli
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