Use the Principle of Induction to prove the formula for all natural numbers (n). (1+2+3+cdots+n=frac{n(n+1)}{2})
Question:
Use the Principle of Induction to prove the formula for all natural numbers \(n\).
\(1+2+3+\cdots+n=\frac{n(n+1)}{2}\)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 0% (1 review)
Inductive proofs have two parts 1 Base Case Show the claim is true for a specific starting point us...View the full answer
Answered By
PALASH JHANWAR
I am a Chartered Accountant with AIR 45 in CA - IPCC. I am a Merit Holder ( B.Com ). The following is my educational details.
PLEASE ACCESS MY RESUME FROM THE FOLLOWING LINK: https://drive.google.com/file/d/1hYR1uch-ff6MRC_cDB07K6VqY9kQ3SFL/view?usp=sharing
3.80+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
In this question we study the recursively defined functions f, g and h given by the following defining equations f(0) = 1 base case 0, f(1) = 0 base case 1, and f(n) = n f(n 1) + f(n 2)^2...
-
Use the Principle of Induction to prove the formula for all natural numbers \(n\). \(1+x+x^{2}+\cdots+x^{n}=\frac{1-x^{n+1}}{1-x}\) for any \(x eq 1\)
-
Use the Principle of Induction to prove the formula for all natural numbers \(n\). \(1+x+x^{2}+\cdots+x^{n}=\frac{1-x^{n+1}}{1-x}\) for any \(x eq 1\)
-
April Moon set a record in flight shooting. In 1981 in Utah, she sent an arrow a horizontal distance of 950 m. What was the speed of the arrow at the top of the flight if the arrow was launched at an...
-
A bicycle with tires 68cm in diameter travels 8.0km. How many revolutions do the wheels make?
-
Smith & Associates are the auditors of Fleur Corp. For the year 2020, Smith set the overall materiality of $1,500,000, and a tolerable misstatement of $750,000. During the year, the identified the...
-
England, Inc., had the following payroll for March: Required Prepare journal entries on March 31 to record: a. Accrual of the monthly payroll. b. Payment of the net payroll. c. Accrual of employer's...
-
Cody Jenkins and Lacey Tanner formed a partnership to provide landscaping services. Jenkins and Tanner shared profits and losses equally. After all the tangible assets have been adjusted to current...
-
B Ltd. sold its assets on January 2, 2024, two days after its December 31, 2023 year-end for $1,300,000. The sale price includes inventory $400,000, land $300,000, and building $600,000. The original...
-
Use the Principle of Induction to prove the formula for all natural numbers \(n\). \(1^{3}+2^{3}+3^{3}+\cdots+n^{3}=\frac{n^{2}(n+1)^{2}}{4}\)
-
Given a finite list of prime numbers \(p_{1}, \ldots, p_{N}\), let \(M=\) \(p_{1} \cdot p_{2} \cdots p_{N}+1\). Show that \(M\) is not divisible by any of the primes \(p_{1}, \ldots, p_{N}\). Use...
-
Redo question 29 using a bar chart. Which method is better for presenting these election results? Question 29 The results of the 1991 city council election (voters could vote for more than one...
-
Protrade Corporation acquired 8 0 percent of the outstanding voting stock of Seacraft Company on January 1 , 2 0 2 0 , for $ 6 0 4 , 0 0 0 in cash and other consideration. At the acquisition date,...
-
Explore the intricacies of inter-process communication (IPC) mechanisms in operating systems, including shared memory, message passing, and synchronization primitives, and their respective trade-offs...
-
7. Use the following information to answer this question: Windswept, Incorporated 2021 Income Statement ($ in millions) Net sales $ 9,150 Cost of goods sold 7,590 Depreciation 435 Earnings before $...
-
What are the challenges and solutions involved in implementing fault tolerance and high availability features in mission-critical operating systems, such as redundancy, failover mechanisms, and...
-
Some managers argued that telework negatively influences employee performance so it should not be used after the COVID-19 pandemic?. Do you agree or disagree with the argument? (Explain why you agree...
-
Thalina Mineral Works is one of the worlds leading producers of cultured pearls. The companys condensed statement of cash flows for the years 20122014 follows. Required Comment on Thalina Mineral...
-
For what reason might an exporter use standard international trade documentation (letter of credit, draft, order bill of lading) on an intrafirm export to its parent or sister subsidiary?
-
Approximate the sum of the series correct to four decimal places.
-
Approximate the sum of the series correct to four decimal places. n+1 ,6 31
-
Approximate the sum of the series correct to four decimal places.
-
A precision lathe costs $20,000 and will cost $30,000 a year to operate and maintain. If the discount rate is 12% and the lathe will last for 5 years, what is the equivalent annual cost of the tool?...
-
Use the following information to complete Schedule M-1 (Form 1120) for ADZ Corporation. ADZ net income per books $350,485 Federal income taxes 98,389 Excess of capital losses over capital gains 3,867...
-
A friend at university notes that you are studying Finance and Investment Management. He asks why ( FNB ) the First National Bank was trading at a share price of R 4 7 . 3 3 and ( STD ) Standard Bank...
Study smarter with the SolutionInn App