Question: a. Prove that for all n E N, 1+2+3+...+ n = n(n + 1) 2 b. Suppose you have a book whose pages are

a. Prove that for all n E N, 1+2+3+...+ n = n(n

a. Prove that for all n E N, 1+2+3+...+ n = n(n + 1) 2 b. Suppose you have a book whose pages are numbered from 1 to 100. Use the formula in part a to find the sum of all of the page numbers in the book. c. Suppose that someone has taken the book from part b and torn out the sheet of paper that had page 53 on one side and page 54 on the other side. What is the sum of all of the remaining page numbers in the book?

Step by Step Solution

★★★★★

3.52 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Proof by mathematical induction Step 1 Base case n 1 For n 1 the lefthand side LHS is 1 and the ri... View full answer

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 Mathematics Questions!

The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...

Suppose a young researcher would like to analyze the relationship between Gross Domestic Product (GDP), foreign direct investment (FDI), and trade openness (OPEN), where GDP is theoretically modeled...

Prove that for all n Z+, n > 3 2n

Air at 35C, and 4m/s is flowing parallel a building wall 40 m long and 8 m high. Wall temperature is maintained at 25C. Assume air properties; Pr = 0.7; v=2.5.0X105, p=1.25 kg/m, k=0.030W/m.K....

(revised 5/17/23 D REQUIRED SUPPLIES AND ANALYSIS TOOLS 0 Meter stick, a clamp with attached hanger to hang meter stick, washers and nuts to serve as weights (you may also use other small objects),...

Please i provided two different homework the second one is already solve. This is to help you understanding how the first one should be done. Instructions: Use these instructions for the remainder of...

Hi please i just solving this problem could you help to finish now the next question 6(1a) Instructions: Use these instructions for the remainder of the exam. Your J-number JN := (K E 0. .9/ k E...

Briefly discuss the cost-volume-profit analysis model and how it is used. Use the attached PDF. APA Citation. 300 words. REVISED PAGES 3 Chapter Three 1 Fundamentals of Cost-Volume-Prot Analysis...

Data gistrun sending inside a pack fills in as conventional allowing subordinate rules to execute on progressive clock cycles. Correspondence between gatherings conventionally causes a surprising...

TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x= 1! x1...

Carbon-14 dating is used to date a bone found at an archaeological excavation. If the ratio of C-14 to C-12 atoms is 3.25 1013, how old is the bone?

A humanitarian aid operation in Somalia requires supplies to be delivered to three inland locations named 1, 2, and 3, whose demands are 500, 600, and 450 tons respectively. The deliveries can come...

If Little Cow Construction places a hedge on its copper production in the futures market, it would contracts for delivery in six months at a delivery price of $4.94 per pound to generate profits that...

The heat capacity at constant pressure of hydrogen cyanide is given by the expression Cp[J/(mol C)] = 35.3 + 0.0291T(C) (a) Write an expression for the heat capacity at constant volume for HCN,...

For an 85 wt% Pb-15 wt% Mg alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 600C (1110F), 500C (930F),...

Calculating Expected Returns A portfolio is invested 10 percent in Stock, 75 percent in Stock 3, - and 15 percent in Stock K. The expected returns on these stocks are 8 percent, 15 percent, and 24...

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. (a) If its height is 4 ft and the...

What is the efficient markets hypothesis, what are its three forms, and what are its implications? MINI CASE Sam Struthers and Shawna Tibbs are senior vice presidents of the Mutual of Seattle. They...

What is the antiderivative 8t5e4t6dt? Do not include the constant "+C" in your answer. For example, if you found that the antiderivative is 2t+C, you would enter 2t.

The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-6. On December 12, Irene purchased the building where her store is located. She paid...

Harold Conners (Social Security number 785-23-9873) lives at 13234 DeMilo Drive, Houston, TX 77052, and is self-employed for 2012. He estimates his required annual estimated tax payment for 2012 to...

Larry and Lisa Williams, both 33 years old, have been married for 9 years. They live at 638 Arctic Way, Fairbanks, AK 99701. Lisa's Social Security number is 445- 81-1423 and Larry's is 798-09-8526....

The current balance on a loan is $3837.30. If the interest rate on the loan is 10% compounded monthly, how long ago was the $2870 loan made?

Rounded to the nearest month, how long will it take an investment to triple if it earns: a. 9% compounded annually? b. 8% compounded quarterly?

Rounded to the nearest month, how long will it take an investment to double if it earns: a. 8.4% compounded annually? b. 10.5% compounded semiannually?