Re: Finding the general term of a sequence

> How do you find the sequence of diameters?

lest talk in radius
the center of C = R
for C1
lest call the center of C1 is Q1
there is a triangle RPQ1 with a 90° corner in P
so 1 + (1 - r1)^2 = (1 + r1)^2
the radius of C1 R1 = 1/4

in general
1 + (1 - 2*Ai - Ri)^2 = (1 + Ri)^2
and Ai = sum{1 -> (i - 1)} Ri = R1 + R2 + ... + R(i - 1)
Ri = (1 - 2*Ai)^2/(4*(1 - Ai))
this gives the following series
{1/4, 1/12, 1/24, 1/40, 1/60, 1/84, 1/112, 1/144, 1/180, 1/220, ...}
so Rn = 1/(2*n*(n + 1))


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