how can i calculate the series using the first 10 terms of the sequence

how can i calculate the series using the first 10 terms of the sequence

[R.D]

term = 0; % initialize variable

% loop 10 times

for n = 0:9

% calculate term

term = (1 / factorial(n));

% display term

fprintf('Term %d = %f\n', n+1, term);

end

[Ameer Hamza]

Which series?

[R.D]

using the first 10 terms

Answer 1

[Ameer Hamza]

try this

term = 0; % initialize variable
% loop 10 times
for n = 0:9
% calculate term
term(n+2) = term(n+1) + (1 / factorial(n));
% display term
fprintf('Term %d = %f\n', n+1, term(n+2));
end

Output

Term 1 = 1.000000
Term 2 = 2.000000
Term 3 = 2.500000
Term 4 = 2.666667
Term 5 = 2.708333
Term 6 = 2.716667
Term 7 = 2.718056
Term 8 = 2.718254
Term 9 = 2.718279
Term 10 = 2.718282

[R.D]

do you think my first one is wrong?

[Ameer Hamza]

Your code is correct, but it didn't add the previous terms of the series. I just changed one line

term = term + (1 / factorial(n));

Rest is same as your code.

[R.D]

Yes but I have different terms from you

Term 1 = 1.000000

Term 2 = 1.000000

Term 3 = 0.500000

Term 4 = 0.166667

Term 5 = 0.041667

Term 6 = 0.008333

Term 7 = 0.001389

Term 8 = 0.000198

Term 9 = 0.000025

Term 10 = 0.000003

[Ameer Hamza]

Yes, I in your code, you only had

term = (1 / factorial(n));

which does not sum the previous terms.

My code have

term = term + (1 / factorial(n));

which sums all previous terms.

[R.D]

so what do you think it's better?

[Ameer Hamza]

"Better" depends on what you are trying to do. If you are trying to estimate Euler number than my code is better, and if you are just trying to see the term of Taylor series of for x = 0, then your code is better.

[R.D]

can you check your email?

[Ameer Hamza]

Can you post it here so that anyone else can also give their input if they want?

[R.D]

The Euler's number (?) is an important mathematical constant that forms the base of the natural logarithms. This number can be obtained in MATLAB by typing: exp(1), in other words, ? to the power of 1. The exact value of ? can be defined by the infinite series:

? = ∑

1 ?!

∞

?=0

where ?! is the factorial of ?.

You are asked to create a MATLAB M-file named “problem1_XXX.m” (exactly like this, without capital letters or spaces, and substituting XXX by your full student number) that

1. uses a FOR loop to display in the Command Window the first 10 terms in the sequence. Hint: the factorial of ? (or ?!) in MATLAB is obtained by typing factorial(n).

2. calculates the series using the first 10 terms of the sequence.

3. obtains the error of the previous series (in %) with respect to the value of ? that is stored in the memory of MATLAB.

4. creates a plot in which the number of terms that are included in the series appears in the abscissa (?) and the result of the series for the corresponding number of terms appears in the ordinate (?). The line should contain ‘x’ markers to indicate each value of the series.

5. includes in the plot useful labels and a line at ? = ? to represent the value to which the series should converge.

[R.D]

this is my exercice

[Ameer Hamza]

Romario, since this is a homework question, so I cannot give you a complete solution. The code in your question is for task 1 of your assignment, and code in my answer corresponds to task 2 (I have modified it to save all values inside for-loop). Based on these results, you can try to solve the next task of your assignment.

[R.D]

so the code 1 that i wrote is correct?

[R.D]

disp('the sum of the first 10 terms is')
disp(term)

%error calculation 
ea=abs(term-exp(1))/exp(1)*100; 
fprintf(' The error is: %f \n', ea)

THOSE ARE CORRECT ARE THE Q2 AND Q3??

[Ameer Hamza]

Yes, It is correct according to the task 1.

[R.D]

How can I solve the Q4? because I tried but nothing

[Ameer Hamza]

It is something like this

term = 0; % initialize variable
% loop 10 times
for n = 0:9
% calculate term
term(n+2) = term(n+1) + (1 / factorial(n));
% display term
fprintf('Term %d = %f\n', n+1, term(n+2));
end
plot(0:10, term, '+-')

[R.D]

Are you sure because I tried the same but I think is incorrect??

[Ameer Hamza]

I think this should be correct according to the assignment.

[R.D]

creates a plot in which the number of terms that are included in the series appears in the abscissa (?) and the result of the series for the corresponding number of terms appears in the ordinate (?). The line should contain ‘x’ markers to indicate each value of the series

I think we have to put also the abscissa x ,ordinate y

[Ameer Hamza]

In graphs, the term abscissa and ordinate are just other names for the x-axis and y-axis. It says, plot number of terms on the x-axis and the value of term on the y-axis. According to this, it is correct.

[R.D]

includes in the plot useful labels and a line at ? = ? to represent the value to which the series should converge.

HOW YOU GONNA SOLVE THE Q5??

[Ameer Hamza]

You can use yline: https://www.mathworks.com/help/matlab/ref/yline.html to draw a line at y=e. You can also add xlabel(), ylabel() and title() to your plot.

[R.D]

HOW CAN I ADD THE XLABEL , YLABEL AND TIITLE TO MY PLOT???

[Ameer Hamza]

xlabel(), ylabel(), and title() are MATLAB's functions. After running plot() add the line

xlabel('iterations')
ylabel('terms')
title('enter label')

[R.D]

Undefined function 'label' for input arguments of type 'char'.

Error in testing (line 35)

label('enter label')

THIS IS WHAT MATLAB APPER ON COMMAND WINDOW

[Ameer Hamza]

There was a mistake, recheck the updated comment.

[R.D]

I DON'T KNOW UNTIL Q4 EVERYTHING WAS FINE

ON Q5 APPEAR ME AN ERROR

[Ameer Hamza]

what is the error?

[R.D]

Undefined function 'label' for input arguments of type 'char'.

Error in testing (line 35)

label('enter label')

[Ameer Hamza]

I updated the comment, the corrent command is title

title('enter label')

[R.D]

Plot all the rain drops on the window when the time is 0 s (i.e. at the start of the journey) using a FOR loop. The plot should be contained exactly in the perimeter of the window and the rain drops should be represented as solid blue lines that connect the corresponding start and end nodes

ANY IDEA HOW TO SOLVE THIS ONE???

[Ameer Hamza]

Romario, please start a new question, since it is entirely different from your original question. Also, for such a homework question. It is a better idea to show us some code that you have tried and ask a specific question related to MATLAB.

Answer 2

[Clara]

Let x0 be any integer. Suppose that the following rule is used to define a sequence of numbers based on x0.

xk+1 =0.5xk (if xk is even)

or xk+1=3xk+1 (if xk is odd)

Write a MATLAB script to generate the first 10 terms of the sequence.

[Voss]

https://www.mathworks.com/matlabcentral/answers/questions/new/?s_tid=gn_mlc_ans_ask

[Walter Roberson]

Collatz Conjecture