Posted by **luckybee** on Sunday, January 8, 2012 at 7:38pm.

in an infinite series of circles the radius of the second circle is one half the radius of the first circle and the radius of the third circle is one half the radius of the second circle. if the first circle has a radius of one inch which of the following statements best describe the sum of the areas of all the circles?

1. the sum of the area of all the circle converge to pi in^2

2. the sum of the areas of all the circles diverge from 2pi in^2

3. the sum of the areas of all the circles converge to 2pi in^2

4. the sum of the areas of all the circles diverge from pi in^2

my solution: i think it is number 4 because the radius ends up being zero.

- math gre question -
**apisit**, Monday, January 9, 2012 at 12:23am
a total of 920 adult and student ticket were sold for the school play. the number of student tickets sold was 16 less than twice the number of adult tickets.how many adult tickets were sold?

- math gre question -
**Steve**, Monday, January 9, 2012 at 5:18am
sum is pi(1^2 + (1/2)^2 + (1/4)^2 + ...)

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

= pi (1/(1 - 1/4)) = pi (1/(3/4)) = 4pi/3

I think the answer they wanted was 2pi (#3) but 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...

and we have 1 + 1/4 + 1/16 + 1/64 + ...

a + s = 920

s = 2a-16

a + 2a-16 = 920

3a = 936

a = 312

s = 308 = 2*312 - 16

## Answer this Question

## Related Questions

- Geomatric series - A fractal is created: A circle is drawn with radius 8 cm. ...
- GEOMETRY CIRCLE - 1.An isosceles triangle with each leg measuring 13 cm is ...
- Geometry - A dartboard consists of five concentric circles. The radius of the ...
- maths - there are two circles touching each other at one point. The radius of ...
- GEOMETRY CIRCLES PLEASE - HELP ME PLEASE. 1.An isosceles triangle with each leg...
- Pre-Calc (Circles). Please help :( - Five concentric circles with radii 1, 2, 3...
- geometry (help steve) - A circle of radius 1 is drawn in the plane. Four non-...
- GEOMETRY CIRCLES PLEASE - 1.An isosceles triangle with each leg measuring 13 cm ...
- Geometry - A circle of radius 1 is drawn in the plane. Four non-overlapping ...
- Math - A circle of radius 1 is drawn in the plane. Four non-overlapping circles ...