Please answer the questions below. True or False? Recursion functions can be pro
ID: 2900284 • Letter: P
Question
Please answer the questions below.
True or False? Recursion functions can be proven using mathematical induction. True False Fibonacci numbers are defined as: fn = fn-1 + fn-2 for n > 1. The first six Fibonacci numbers are: 0, 1, 2, 3, 5, 8. What is the next Fibonacci number? 11 13 15 None of the above Find f(4) if f is defined recursively by: f(0) = f(l) = 1 and f (n +1) = f (n)2 + f (n -1)3 for n > 1. 1 2 29 33 True or False ? The following proposed definition of a recursive function is valid for n > 1: f(0) = 0, f(l) = 1, f(n) = 2f(n+1). True False An investor begins to save in 1990 with $500. Each year, the savings increases 10% over the year before, and the investor contributes another $100. Write a recurrence relation and initial conditions on sn, the amount of savings n years after 1990. Use this relation to determine the amount saved by 1994. $1,196.15 $ 996.50 $ 732.05 $1,415.77 True or False? In programming a recursive algorithm, the algorithm must call itself with smaller input. True False What is the result of the following recursive algorithm? procedure unknown(n:positive integer) if n = 1 then unknown(n) := 1 else unknown(n) := unknown(n-1) + n end procedure n + n-1 = 2n - 1 n sum of n positive integers zero Find the sequence for the recursive formula: sn = -sn_, +10, s0 = -4 -4,14,-4,14,... -4, 9, -3, 11, ... -4, 5, 10, -4, 5, 10,... not a recursive formula Find the sequence for the following closed formula: sn = 9(-l)"+l + 5 for n = 0, 1, 2, 3 5,-9, 5, 9 6, 14, 86, 734 -4, 14, -4, 14 -4,-4,-4,-4 Consider the recursive algorithm for Fibonacci numbers: procedure fib(n:nonnegative integer) if n = 0 then fib(0) := 0 else if n = 1 then fib(1) := 1 else fib(n) := fib(n-l) + fib(n - 2) end procedure How many additions does it take to find f(7), the eighth Fibonacci number? (assume f(0) is the first Fibonacci number) 8 10 6 20Explanation / Answer
1) True
2) b)13
3) d)33
4) True
5) a.1196.5
6) False
7) c
8) a
9) c
10) d.20