Home / Questions / The figure shows two circles C and D of radius 1 that touch at P. T is a common
The figure shows two circles C and D of radius 1 that touch at P. T is a common tangent line; C_{1} is the circle that touches C, D, and T; C_{2} is the circle that touches C, D, and; is the circle that touches C, D, and C_{2}. This procedure can be continued indefinitely and produces an infinite sequence of circles {C_{n}}. Find an expression for the diameter of { C_{n}} and thus provide another geometric demonstration of Example 6.
EXAMPLE 6 Show that the series is convergent, and find its sum.
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