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mathslover

  • 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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  1. ParthKohli
    • 2 years ago
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    \[\pi + {\pi \over 4} + {\pi \over 16}\cdots\]

  2. ParthKohli
    • 2 years ago
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    Hmm...

  3. mathslover
    • 2 years ago
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    You mean to say like this : \[\large{S = \pi + \frac{\pi }{4} + \frac{\pi}{16} + .... }\]

  4. mathslover
    • 2 years ago
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    But what next?

  5. ParthKohli
    • 2 years ago
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    I think it's approaching something.

  6. mathslover
    • 2 years ago
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    Well i think we can take : infinite geometric progression ...

  7. mathslover
    • 2 years ago
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    pi ( 1 + 1/4 + 1/16 + .... )

  8. ParthKohli
    • 2 years ago
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    Where did you get this question?

  9. ParthKohli
    • 2 years ago
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    http://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%C2%B7_%C2%B7_%C2%B7

  10. mathslover
    • 2 years ago
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    I have a book, Math IQ Challenge

  11. ParthKohli
    • 2 years ago
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    It'd be \(\dfrac{4}{3}\pi\)

  12. ParthKohli
    • 2 years ago
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    lol - we solved it before asking it on M.SE :)

  13. mathslover
    • 2 years ago
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    :) \[\large{ S _\infty = \frac{a}{1-r}}\] -- infinite geometric series a = 1 r = 1/4 1 / ( 1- 1/4 ) = 1/ (3/4) = 4/3

  14. mathslover
    • 2 years ago
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    Yeah ... thanks @ParthKohli

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