I'm not sure how to relate a counter

Hi Saskiaa, if the question is just "how to have j = 1, 2, 3 ... when n = 0, 1, 2 ..." it is enough to write the loop with respect of one of the two variables (namely n) and then compute the other, for instance:

for n = 0 : 9
    j = n + 1;
    % some other computation
end

However, I guess that in your particualr example the problem is that 0! = 1! = 1. You could handle separately the case n=0 by rewriting the sum like:

This gives something like:

value = 1.0;
fact = 1.0;
for n = 1 : 10
    fact = fact * n;
    value = value + 1/fact;
end
fprintf('sum = %20.15f  (reference = %20.15f)\n', value, exp(1));
sum =    2.718281801146385  (reference =    2.718281828459045)

Notice that this kind of code is for pedagogical purpose only. In "true" Matlab coding, I would rather vectorize like that:

fact = cumprod(1:10);
value = 1.0 + sum(1./fact);
fprintf('sum = %20.15f  (reference = %20.15f)\n', value, exp(1));
sum =    2.718281801146385  (reference =    2.718281828459045)

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Saskiaa Vamadevan 2022-4-7

This is what I did, but I'm not getting the correct answer, in the sense that when it's plotted, it's not near the exp which suggests my other answers are also incorrect. When I plot this, my highest value is 1.7 not 2.7. I tried the what you suggested but got the same outcome. I have to somehow include 0! in the equation but I don't know how to via relating the counter. I did try what was suggested.

clear

sv=0;

sumtoplot = zeros(1,10);

for n = 1:10 % Set up a FOR loop for counter n

term = 1 / factorial(n);

disp(term)

sv = sv + term;

sumtoplot(n) = sv;

end

disp('This is the sum of the series')

disp(sv)

% Calculate the error of the series

errorseries = (sv-exp(1))*100/exp(1);

disp('This is the error in %')

disp(errorseries)

% Create a plot of the series based on the number of terms in the

% sequence

ordersequence = 1:10;

plot(ordersequence,sumtoplot,'b-x')

hold on

% Where the series should converge

plot([1,10],[exp(1),exp(1)],'k-')

hold off

% Customise the plot

xlabel('Number of terms in the series')

ylabel('Value of the series')

legend('1/n!','e')

Riccardo Scorretti 2022-4-7

在 MATLAB Online 中打开

Let's see that (by the way, it would be better if you format your code... as a code).

The problem is fundamentally that your loop has to start from 0, not to 1. By starting the loop from 1, you are missing the term 1/0! = 1/1 = 1, which explains why you get a value close to 1.7 instead of 2.7. By doing this, if you want to limit to n = 10, the size of sumtoplot must be 11 (= 10+1), and when you access to if in the first loop, you must use sumtoplot(n+1):

clear

sv=0;

sumtoplot = zeros(1,10+1);

for n = 0:10 % Set up a FOR loop for counter n % ***

term = 1 / factorial(n);

disp(term)

sv = sv + term;

sumtoplot(n+1) = sv; % ***

end

1 1 0.5000 0.1667 0.0417 0.0083 0.0014 1.9841e-04 2.4802e-05 2.7557e-06 2.7557e-07