Question regarding continued fractions

Reference no: EM13131029

Show that each of the following holds:

[1,1,1,1,1,1,....]^2 = [2,1,1,1,1,1,....]

[1,2,2,2,2,2,....]^2 = [2]

[1,1,1,1,1,1,....][0,1,1,1,1,1,....] = [1]

In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).

Note:We can write down any continued fraction such as
P/Q = a + 1/(b + 1/(c + 1/(d + ...)))

just as a list of the numbers a, b, c, ... Since the first number, a, is special (it is the whole number part of the value) it is separated from the rest by a semicolon (;) and the rest are written as a list with comma separators (,) like this:

P/Q = [a; b, c, d, ...]

Reference no: EM13131029

Questions Cloud

Separate acids in a solution of water : How do I determine the concentration of 2 separate acids in a solution of water if I know the overall pH of the solution? There exists both formic acid and acetic acid in a 1 liter solution of water. The overall solution pH is stated as 4.0 and it ..

What is thompson accounts receivable turnover : Evaluate the following scenarios, assuming both companies use the accounts receivable method of estimating bad debts expense.

Probability that seven or more vehicles carry just driver : Winnipeg during rush hour are occupied by just the driver. If you choose 12 vehicles at random, what is the probability that 7 or more carry just the driver?

Evaluate the impact to a business : Evaluate the impact to a business when compensation, such as sales commissions and bonus, are tied to achieving budgeted expectations. Suggest how management can prevent employees from manipulating results.

Question regarding continued fractions : In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).

How much will patti have in the account : At the end of each quarter, Patti deposits $500 into an account that pays 12% interest compounded quarterly. How much will Patti have in the account in three years?

What exactly is an alkane and alkene : What exactly is an alkane and alkene? What is an ester?? does it relate to anything above?

Determine total production cost per unit for each product : Using direct labor hours as the basis for assigning overhead costs, determine total production cost per unit for each product line.

Find probability all the hotel-s rooms will be rented : Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30. What is the probability all the hotel's rooms will be rented?

User Account

All Pages