## 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 ?

1. ParthKohli

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

2. ParthKohli

Hmm...

3. mathslover

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

4. mathslover

But what next?

5. ParthKohli

I think it's approaching something.

6. mathslover

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

7. mathslover

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

8. ParthKohli

Where did you get this question?

9. ParthKohli
10. mathslover

I have a book, Math IQ Challenge

11. ParthKohli

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

12. ParthKohli

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

13. mathslover

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

14. mathslover

Yeah ... thanks @ParthKohli