Question: Consider the following Python function foo, which takes as input an integer n21 and returns a tuple of length 2 of integers: def foo(n): assert

Consider the following Python function foo, which takes as input an integer n21 and returns a tuple of length 2 of integers: def

Consider the following Python function foo, which takes as input an integer n21 and returns a tuple of length 2 of integers: def foo(n): assert n>=1 if n 1: return (1, 2) else: p, a foo(n-1) return (q + p*n* (n+1), q*n* (n+1)) Prove that for n21, foo(n) (p, q) such that 1 1 9 n+1 (Hint: induction on n.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Consider the following recursive function foo which takes as input a positive integer n: def foo ( n ) : if n = = 1 : return 1 if n % 2 = = 0 : return n + foo ( n / / 2 ) return foo ( 3 * n + 1 ) Can...

I have never learned Python before and we have not touched on this in class yet! Please help! 1) Consider the Python list A = [4, 8, 15, 16, 23, 42]. Let D(i,n)D(i,n) be the propositional function...

Overview. Write a program to implement the RSA public - key cryptosystem. The RSA ( RivestShamir - Adleman ) cryptosystem is widely used for secure communication in browsers, bank ATM machines,...

The objective of this homework set is to get you started writing Python code. First, check out the factorial program in Newman, in exercise 2.13 (page 83 in my edition). (We're just using the...

(a) Returns True if the first half of a is the same as the reversal of the second half of s and False b) Returns True if the first half of the string a is the same as the second half and False ot...

Although this function could be completed in one line, you must use the following template: def first_and_last(values): put your docstring here" first = last = return [first, last] Here are some...

* Install the Python library ` pycryptodome ` by executing the following in a code cell. ` ` ` ! pip install pycryptodome ` ` ` * Import some functions we will use by executing the following code. (...

Write a Python function count_rectangles that takes as arguments positive integers m and n and returns the number of distinct, non-degenerate rectangles in an integer grid with vertical lines at x...

2 Basic List Manipulations Problem 1 (5 points) Write an ML function, called alternate: 0a list ? 0a list ? 0a list, that takes two lists, having the same length, as input and produces an output list...

What do you understand by Thales discovered nature? Explain, citing examples.

According to the Coase theorem, private parties can solve the problem of externalities if a. the cost of bargaining is large. b. the initial distribution of legal rights favors the person causing the...

At December 3 1 , year 1 , Discount Taco Supply reported accounts receivable of $ 7 0 0 , 0 0 0 and an allowance for uncollectible accounts of $ 5 0 , 0 0 0 . During year 2 , sales on account totaled...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

Question How are VEBA assets allocated when a plan terminates?

Question May a taxpayer roll over money from an IRA to an HSA?

Question What is the doughnut hole in HSA coverage?