. Use Stirling’s approximation x! ∼ (2π)1/2x(x+1/2)e−x as in Section 6.5 to find the corresponding approximation for bn in XXXXXXXXXXUse this to find an approximation for b100.   . Suppose dab, dac...

.
Use Stirling’s approximation

x! ∼ (2π)1/2x(x+1/2)e−x

as in Section 6.5 to find the corresponding approximation for bn in (12.1). Use

this to find an approximation for b100.

.
Suppose dab, dac and dbc are distances that form an additive tree

for the unrooted tree with leaves {a, b, c}. (There is only one such tree.) The

tree has length x for the leaf a, length y for the leaf b and length z for the leaf

c. Derive a formula for x, y and z in terms of dab, dac and dbc. [Hint: Draw a

picture.]