A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees wit
h n vertices.
(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?
(b) For general n, derive a recurrence relation for Bn.
(c) Show by induction that Bn is (2n). 2.14. You are given an array of n elements, and
(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?
(b) For general n, derive a recurrence relation for Bn.
(c) Show by induction that Bn is (2n). 2.14. You are given an array of n elements, and
1 answer:
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Answer:
future value = 232369.1361
return % = 384.10 %
Explanation:
given data
principal = $100 per month
time = 40 year = 480 months
rate = 6.25 % yearly = 0.0625 yearly = 0.005208 monthly
to find out
total amount of capital at the end of your investment and percentage is your total return
solution
so here future value formula is
future value = P ..........1
here r is rate and t is time and P is principal
so put all value
future value = 100
future value = 232369.1361
so
Total capital at the end of investment-Total principle invested over the years
232369.1361 - 100 ( 12 × 40 )
184369.1361
so
Return % = × 100
return % = 384.10 %