Question: 3. Show that (12) + (2.3) + (3.4)+...+ n(n+1) = n(n+1)(n+2) 3 for all natural numbers n = 1,2,3

3. Show that (12) + (2.3) + (3.4)+...+ n(n+1) = n(n+1)(n+2) 3 for all natural numbers n = 1,2,3

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To prove the given identity 1 23 34 nn1 nn1n23 We can use mathematical ind... View full answer

blur-text-image
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!

Q:

References: Health Information Management Case Studies Second Edition AHIMA by Dianna M. Foley Health Information Management Technology an Applied Approah Sixth Edition AHIMA by Nanette Sayles and...

Q:

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

Q:

If you dissolve 8.14 grams of calcium chloride, CaCl 2 , in enough water to make 125.0 mL of solution, what is the molarity of the solution?

Q:

prove the following using mathematical induction EXAMPLE 1 Prove that, for any positive integer n, 1+ 2+ 3+...+ /= n(n +1) 2 Solution: n 1+ 2 13 +. .. + 10 = 10 (10+1) Step 1: P (1 ) 2 1 = 1(1+1) =...

Q:

MATHEMATICAL INDUCTION CJ Cambre Jr. [COMPANY NAME] [Company address] Carlos Cambre Professor Nickerson MAT 403 December 9, 2016 Mathematical Induction Pierre de Fermat really knew he used...

Q:

Answer part (a) of Exercise 14 if the numbers are arranged in a circle, and, as we count clockwise about the circle, none of the patterns 12, 23, 34, ..., (n - 1)n, n1 occurs. Exercise 14 In how many...

Q:

# of Subscribers # of Enrolled 5 8 9 18 105 217 58 128 2 3 433 822 6 8 21 IN 3 11 23 8 15 26 40 316 316 2 3 1 3 11 18 12 23 26 49 6 10 1 7 7 4 10 13 25 2 2 17 23 7 10 12 14 17 43 1129 1868#...

Q:

INDE 2333 Engineering Statistics I Practice Exam 2 INDE 2333 Engineering Statistics I - Practice Exam 2 Instructions: This is an individual effort closed note, closed book, open table exam. You have...

Q:

Mathematics 220 Homework 7 Due March 3/4 1. Question 6.2. Prove that any non-empty subset of a well-ordered set of real numbers is well-ordered. 2. Prove that for all n N 1 1 n 1 + ++ = . 12 23 n(n +...

Q:

MEAN 6.0000 WHEN WE HAVE LARGE DATA SETS, WE GROUP THE DATA. IN THIS CASE OUR GROUPS WILL BE: STD DEV 2.17 IN A NORMAL DISTRIBUTION THE MEAN, MEDIAN AND MODE ARE ALL THE SAME NUMBER X-VALUES Z-VALUES...

Q:

Reconsider the network diagram of Problem 1 a. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is half finished....

Q:

Discuss and analyze how government regulation has developed and how it affects consumerism and citizens. Along the way, discuss the politics of regulation in affecting public policies. Performance...

Q:

If f ( x ) = x e x , find f ' ( 0 ) 1 e 1 1 - 6 0

Q:

A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement,...

Q:

How would you use a Grignard reaction on an aldehyde or ketone to synthesize the following compounds? (a) 2-Pentanol (b) 1-Butanol (c) 1-Phenylcyclohexanol (d) Diphenyl methanol

Q:

Determine the ratio a/b for which the shear force will be zero at the midpoint C of the beam. B. - b2 - b/2

Q:

Two atmospheric sound sources A and B emit isotropically at constant power. The sound levels F of their emissions are plotted in Figure versus the radial distance r from the sources. The vertical...

Q:

Passengers in an auto traveling at 16.0 m/s toward the east hear a siren frequency of 950 Hz from an emergency vehicle approaching them from behind at a speed (relative to the air and ground) of 40.0...

Q:

A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and...

Q:

Transform polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = 2

Q:

True or False If f and g are inverse functions, the domain of f is the same as the range of g.

Q:

Determine algebraically whether the function is even, odd, or neither. 5x f(x) x2 - 9

Q:

Consider the isentropic flow on the airfoil. The free-flow condition is At a certain point on the airfoil, the pressure is 3.6 104 N/m2. Calculate the density at this point. Too =

Q:

Considering the normal shock wave in the air, its upstream flow character-istics are Calculate the velocity, temperature, and pressure downstream of the shock wave. U1 = 680 m/s, T = 288 K, and pi =...

Q:

If the 1/7 exponential law is used for the velocity profile Prove that the displacement thickness and momentum loss thickness of the boundary layer are delta Therefore, for the flat, us || | = 96 (3)