(a) Male honeybees are from single parent families; they are from unfertilized eggs so only have mothers. Female honeybees are from two parent families; they are from fertilized eggs so have both mothers and fathers. Let Bn bethe number of nth generation ancestors of a male honeybee. For example: B1 = 1 (itself), B2 = 1 (its mother), B3 = 2 (its grand-father and grand-mother), etc. Find a recurrence relation for Bn. [Assume that no honeybee appears more than once in the ancestral tree; that is, each honeybee has at most one child in the tree.](b) Prove that if n is divisible by four then Bn is divisible by three. (a) Male honeybees are from single parent families; they are from unfertilizedeggs so only have mothers. Female honeybees are from two parent families;they are from fertilized eggs so have both mothers and fathers. Let Bn bethe number of nth generation ancestors of a male honeybee. For example:B₁ = 1 (itself), B₂ = 1 (its mother), B3 = 2 (its grand-father and grand-mother), etc. Find a recurrence relation for Bn.[Assume that no honeybee appears more than once in the ancestral tree; that is,each honeybee has at most one child in the tree.](b) Prove that if n is divisible by four then B₁ is divisible by three.

Let Bn be the number of nth generation ancestors of a male hobeybee. Then we have B1=B2=1. Now for…

Answered: (a) Male honeybees are from single…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(a) Male honeybees are from single parent families; they are from unfertilized eggs so only have mothers. Female honeybees are from two parent families; they are from fertilized eggs so have both mothers and fathers. Let Bn be
the number of nth generation ancestors of a male honeybee. For example: B1 = 1 (itself), B2 = 1 (its mother), B3 = 2 (its grand-father and grand-mother), etc. Find a recurrence relation for Bn. [Assume that no honeybee appears more than once in the ancestral tree; that is, each honeybee has at most one child in the tree.]
(b) Prove that if n is divisible by four then Bn is divisible by three.