2. The Fibonacci sequence is defined as
f(n) = f(n - 1) + f(n - 2)
with f(0) = 0 and f(1) = 1.
Find f(54) by a program or maually. Note that this number must
be positive
and f(53) = 53.......73 (starting with 53 and ending with 73).
I must admit that
my three machines including a desktop are unable to find f(54)
and they
quit during computation.
The answer is f(54) = 86267571272
*/
The Java code:
public...
Prove these scenarios by mathematical induction:
(1) Prove n2 < 2n for all integers
n>4
(2) Prove that a finite set with n elements has 2n
subsets
(3) Prove that every amount of postage of 12 cents or more can
be formed using just 4-cent and 5-cent stamps
Prove the following:
Let f(x) be a polynomial in R[x] of positive degree n.
1. The polynomial f(x) factors in R[x] as the product of
polynomials of degree
1 or 2.
2. The polynomial f(x) has n roots in C (counting multiplicity).
In particular,
there are non-negative integers r and s satisfying r+2s = n such
that
f(x) has r real roots and s pairs of non-real conjugate complex
numbers as
roots.
3. The polynomial f(x) factors in C[x] as...
Let function F(n, m) outputs n if m = 0 and F(n, m − 1) + 1
otherwise.
1. Evaluate F(10, 6).
2. Write a recursion of the running time and solve it
. 3. What does F(n, m) compute? Express it in terms of n and
m.