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 ?

Question

parthkohli · Answer

$$\pi + {\pi \over 4} + {\pi \over 16}\cdots$$

parthkohli · Answer

Hmm...

mathslover · Answer

You mean to say like this : 

$$\large{S = \pi + \frac{\pi }{4} + \frac{\pi}{16} + .... }$$

mathslover · Answer

But what next?

parthkohli · Answer

I think it's approaching something.

mathslover · Answer

Well i think we can take : infinite geometric progression ...

mathslover · Answer

pi ( 1 + 1/4 + 1/16 + .... )

parthkohli · Answer

Where did you get this question?

parthkohli · Answer

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

mathslover · Answer

I have a book, Math IQ Challenge

parthkohli · Answer

It'd be $\dfrac{4}{3}\pi$

parthkohli · Answer

lol - we solved it before asking it on M.SE :)

mathslover · Answer

:) $$\large{ S _\infty = \frac{a}{1-r}}$$ -- infinite geometric series 

a = 1

r = 1/4

1 / ( 1- 1/4 ) = 1/ (3/4) = 4/3

mathslover · Answer

Yeah ... thanks @ParthKohli