Show that the sequence defined by a1 = 1, an+1 = 3 - 1/an Is increasing and
Question:
a1 = 1, an+1 = 3 - 1/an
Is increasing and an < 3 for all n. Deduce that {an} is convergent and find its limit.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (18 reviews)
a 1 1 a n 1 3 1 a n we show by induction that a n is inc...View the full answer
Answered By
Mugdha Sisodiya
My self Mugdha Sisodiya from Chhattisgarh India. I have completed my Bachelors degree in 2015 and My Master in Commerce degree in 2016. I am having expertise in Management, Cost and Finance Accounts. Further I have completed my Chartered Accountant and working as a Professional.
Since 2012 I am providing home tutions.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Calculus questions
-
Show that the sequence defined by an1 = 2, an+1 = 1/3 an satisfies 0 < an < 2and is decreasing. Deduce that the sequence is convergent and find its limit.
-
Find the first 40 terms of the sequence defined by and a1 = 11. Do the same if a1 = 25. Make a conjecture about this type of sequence. if a, is an even number Sta, 3a, +1 if a, is an odd number
-
Show that the sequence of polynomials converges uniformly on any compact subset S . x2 2! 3! + k=0
-
trade on the common stock of Taz, Inc. that have a strike price of $ 51.00 and a premium of $ 1.00 . In each of the next four parts, calculate the net profit (or loss) on the option position. Note:...
-
Harper acquires 40 percent of the outstanding voting stock of Kinman Company on January 1, 2014, for $210,000 in cash. The book value of Kinmans net assets on that date was $400,000, although one of...
-
In 2002 Adele Lawson purchased a pastel for $29,000 from a dealer, London Arts Group. London Arts Group gave Lawson the following writing, signed by its Director that stated: "This is to certify that...
-
The cross-sectional area of a rectangular duct is divided into 16 equal rectangular areas, as shown in Fig. P5.23. The axial fluid velocity measured in feet per second in each smaller area is given...
-
The following accounts were taken from the financial statements of Orville Company. ______ Interest revenue ______ Common stock ______ Utilities payable ______ Accumulated depreciationequipment...
-
The Conference Board Economic Forecast for the US Economy August 02, 2023 | Report The Conference Board forecasts that the growth seen in many parts of the economy will gradually buckle under...
-
A simple unity feedback control system has a process transfer function The system input is a step function with an amplitude A. The initial condition of the system at time t0 is y(t0) = Q, where y(t)...
-
Find the limit of the sequence {2, 2 2, 2 2 2.....}
-
(a) Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age 2 months. If we start with one newborn...
-
Predict the shape of photometric titration curves (after correction for volume change) ifat the wavelength selectedthe molar absorptivities for the analyte A, the titrant T, and the product P are as...
-
Question 1 (15 marks) A large steel plate is being lowered into position by a crane and is attached to the crane via a cable sling, see Figure Q1. It can be considered to be in equilibrium. The steel...
-
QUESTIONS: a. Sort the carriers in decending order by their current year 's percentage of on-time deliveries. Which carrier is providing the best service in the current year? Which carrier is...
-
You long 10 ATM straddle Ie 10 call and 10 put both at strike of 100. What is the delta and gamma value of the position?
-
3. For the continuous beam shown, determine the support reactions at pin support A, and roller supports B and C. 80 lb/ft 4 ft 400 lb 2 ft 2 ft
-
Present a 2 to 4 minute (closer to 4 minutes than to 2) speech to inform the audience on why you chose your career or field of study . Describe the scope and principal features of the field and...
-
Exercises refer to the graphs of the functions f (x) and g (x) in Fig. 2. Determine h(1) and h(1). 3 Q1 Y 0 y = f(x) CO X
-
Eleni Cabinet Company sold 2,200 cabinets during 2011 at $160 per cabinet. Its beginning inventory on January 1 was 130 cabinets at $56. Purchases made during the year were as follows: February . 225...
-
Prove the identity. 2 tan 0 tan 20 = 1- tan0
-
Write the sum in sigma notation. 1 x + x 2 x 3 + + (1) n x n
-
Use the formula in Exercise 89 to prove the addition formula for cosine. cos( ) = cos cos + sin sin
-
A corporation issues 13 %, 15-year bonds with a par value of $570,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 11%, which implies a selling price...
-
If you were asked whether a large university such as Tennessee or Michigan with a large seating capacity for their football stadiums should build a new football stadium, how would you respond and...
-
A production department reports the following conversion costs. Equivalent units of production for conversion total 436,000 units this period. Calculate the cost per equivalent unit of production for...
Study smarter with the SolutionInn App