Posted by **infinite number of circles** on Saturday, March 16, 2013 at 8:30am.

On a straight line ℓ, we have an infinite sequence of circles Γn, each with radius 1/2^n, such that Γn is externally tangential to the circles Γn−1,Γn+1 and the line ℓ. Consider another infinite sequence of circles Cn, each with radius rn, such that Cn is externally tangential to Γn,Γn+1 and ℓ. The expression ∑i=1 to ∞ ri can be expressed as a−√b, where a and b are positive integers. What is the value of a+b?

Clarification: In this problem, we have a row of circles placed on a line. All points of tangency are distinct. The circle Cn is uniquely determined

## Answer This Question

## Related Questions

- math - Let AB be the diameter of circle Γ1. In the interior of Γ1, ...
- math - Two congruent circles Γ1 and Γ2 each have radius 213, and the ...
- Math - Let AB be the diameter of circle Γ1. In the interior of Γ1, ...
- Math - Γ 1 is a circle with center O 1 and radius R 1 , Γ 2 is a ...
- circle geometry - Circles Γ1 and Γ2 intersect at 2 distinct points A ...
- geometry - Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A...
- GEOMETRY......circle - Circles Γ1 and Γ2 intersect at 2 distinct ...
- math - Equilateral triangle ABC has a circumcircle Γ with center O and ...
- maths - Equilateral triangle ABC has a circumcircle Γ with center O and ...
- Math (please help steve) - Circles Γ1 and Γ2 have centers X and Y ...

More Related Questions