Let f(n) be the sum of the first n terms of the sequence 0, 1, 1, 2,
Question:
Let f(n) be the sum of the first n terms of the sequence 0, 1, 1, 2, 2, 3, 3, 4, . . ., where the nth term is given by
Show that if x and y are positive integers and x > y then xy = f(x + y) = f(x - y).
Transcribed Image Text:
an n/2, if n is even if n is odd (n-1)/2,
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 87% (8 reviews)
f1 0 f2 1 f3 2 4 4 n4 In general fn See below for a proof of this x y and x y are either b...View the full answer
Answered By
Ajeet Singh
Hi there! Are you looking for a committed, reliable, and enthusiastic tutor? Well, teaching and learning are more of a second nature to me, having been raised by parents who are both teachers. I have done plenty of studying and lots of learning on many exciting and challenging topics. All these experiences have influenced my decision to take on the teaching role in various capacities. As a tutor, I am looking forward to getting to understand your needs and helping you achieve your academic goals. I'm highly flexible and contactable. I am available to work on short notice since I only prefer to work with very small and select groups of students. Areas of interest: Business, accounting, Project management, sociology, technology, computers, English, linguistics, media, philosophy, political science, statistics, data science, Excel, psychology, art, history, health education, gender studies, cultural studies, ethics, religion. I am also decent with math(s) & Programming. If you have a project you think I can take on, please feel welcome to invite me, and I'm going to check it out!
5.00+
4+ Reviews
24+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Show that, if X and Y are random variables taking on only two values each, and if E(XY ) = E(X)E(Y ), then X and Y are independent.
-
Show that, if X and Y are random variables taking on only two values each, and if E(XY ) = E(X)E(Y ), then X and Y are independent. Discuss.
-
If X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional distribution of X given that X + Y = m is the hypergeometric...
-
You are the VP of Human Resources for a company with 250 employees. You have both outside sales representatives and inside sales representatives that work primarily by phone. James is an outside...
-
Below is some information about ten respondents to a mail survey concerning candy purchasing. Use SPSS to construct the four different types of cross-tabulation tables which are possible. Label each...
-
To entice a new Chief Operating Officer to leave her current job, a publicly traded stock brokerage firm wants to extend credit to her in the following situations: The company will lend $100,000 to...
-
A channel has a rectangular cross section, a width of \(40 \mathrm{~m}\), and a flow rate of \(4000 \mathrm{~m}^{3} / \mathrm{s}\). The normal water depth is \(20 \mathrm{~m}\). The flow then...
-
Adcock Company issued $600,000, 9%, 20-year bonds on January 1, 2014, at 103. Interest is payable semiannually on July 1 and January 1. Adcock uses straight-line amortization for bond premium or...
-
1. Optimize the following Boolean function F together with the don't care conditions d. F(x, y, z, t) IIM(1, 5, 7, 8, 9, 11, 13) = F(x,y,z,t)=Em(0, 4, 6, 12) (a) (4 points) Draw four-variable...
-
Proctor Power has fixed assets worth $200 million and net working capital worth $100 million. It is financed partly by equity and partly by three issues of debt. These consist of $250 million of...
-
Express as a rational number. k=1 (3k+1- 6k 2k+1)(3k - 2k)
-
(a) You delete a finite number of terms from a divergent series. Will the new series still diverge? Explain your reasoning. (b) You add a finite number of terms to a convergent series. Will the new...
-
Estimate the molar flow rate (kmol/min) of each element in the coal (other than those in the ash).
-
adjusting journal entry ALIF - 1,760 LIMERICK CORPORATION NO. 238 Eastbrook. Alberta. December 15, 20XX PAY TO The ORDER OF EAST WEST COLLEGE $ 44.100.00 --Forty-Four Thousand One Hundred- -00/XX...
-
Explain in bullet points an organisational policy/procedure for a customer complaint, such as a coffee shop
-
How can you use zero-coupon yields to calculate implied one-year forward rates? Give an example.
-
explain why Innovative changes to the current employee value proposition and employee lifetime value approaches may lead to higher employee loyalty
-
Tides are just really, really, long waves. Consider the M2 tide, which has a period of about 12.5 hours. This tide propagates around the world's oceans, which have a depth on the order of 4 km (for...
-
Compare and contrast economic systems with political and legal systems.
-
Smthe Co. makes furniture. The following data are taken from its production plans for the year. Required: 1. Determine the hazardous waste disposal cost per unit for chairs and for tables if costs...
-
(a) If f(x) = 3 x+1 and g(x) = 2 x+2 , graph f and g on the same Cartesian plane. (b) Find the point(s) of intersection of the graphs off and g by solving f(x) = g(x). Round answers to three decimal...
-
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 x log2 x = 4
-
The domain of a one-to-one function g is [0, 15], and its range is (0, 8). State the domain and the range of g -1 .
-
4) Consider the two-stage RK method a. Yn+1 = Yn + h (bf (xn, Yn) + b2f (xn + Ch, Yn + A21hf (xn, Yn))). Show that the truncation error is T = Tn 1 1 - hy" (xn) + hy''' (xn) bh[C2fx + A21fyf] 6 1 -bh...
-
At a large local manufacturer, 200 job applicants completed a qualification test with a mean of 70 and a standard deviation of 5. If only the top 20% of the applicants are chosen, what is the minimum...
-
When Alex changes roles, what should occur?
Study smarter with the SolutionInn App