Question Details

(solution) Compute the value of e. e is the base of the Natural Logarithms.


see attached for more details: Greatly appreciate your help.

3.4.0 or 3.4.3 python version.


Compute the value of e.

 

e is the base of the Natural Logarithms. The first few digits of e are:

 

2.7182818284590452353602874713527

 

There are many ways of calculating the value of e, but none of them ever give an exact answer,

 

because e is irrational (not the ratio of two integers).

 

But it is known to over 1 trillion digits of accuracy! Method 1:

 

For example, the value of (1 + 1/n)n approaches e as n gets bigger and bigger: n

 

1

 

2

 

5

 

10

 

100

 

1,000

 

10,000

 

100,000 (1 + 1/n)n

 

2.00000

 

2.25000

 

2.48832

 

2.59374

 

2.70481

 

2.71692

 

2.71815

 

2.71827 In the equations that follow, "!" means factorial.

 

0! = 1, 1! =1, 2! = 2?1 = 2, 3! = 3?2?1 = 6, 4! = 4?3?2?1 = 24, 5! = 5?4?3?2?1 = 120, etc. Method 2:

 

The Taylor series for the exponential function ex at a = 0 is If x is one, the value of e is equal to 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! + ... (etc)

 

? Another way of expressing this series is the formula: =? 1 =0 ! The first few terms add up to: 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 = 2.718055556 Method 3:

 

Recently, new formulae have been developed by Brothers (2004) makes the calculation of e very

 

efficient. =? ? =0 2+2

 

(2+1)! Your assignment is write a program that computes the value of e using all three of the methods

 

described above. Use values of 1, 2, 5, 10, 100, 1000, and 10000 for the first method, and values

 

of n = 1,2,3,4,5,6,7,8,9,10, and 20 for the second method and values of n = 1, 3, 5, 7, and 9 for

 

the third method. Your program must print out the value of e computed with each value of n for

 

each method and the difference with the value of in math library. Make certain that the outputs

 

are labeled as to which method is being used and what value of n was used.

 


Solution details:

Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .
SiteLock

About this Question

STATUS

Answered

QUALITY

Approved

DATE ANSWERED

Sep 13, 2020

EXPERT

Tutor

ANSWER RATING

GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

  • As a reference for in-depth understanding of the subject.
  • As a source of ideas / reasoning for your own research (if properly referenced)
  • For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).
This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.

NEW ASSIGNMENT HELP?

Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.

Order Now