I'm not sure how to relate a counter

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I have a equation:
𝑒 = ∑ 𝑛!
n = 0
I need to some how relate the counter, which starts at 1, with the factorial n that starts at 0. But I'm not sure how to go about this.
I need to make j=1 when n=0 and so on j=1,2,3,4,5,6... when n=0,1,2,3,4.....
i have to do this via for loops to get the first 10 terms of the sequence as well as calulating the series then plotting it.
I'm not sure how to relate the counters, how to make j=1 when n=0 and so on.

Answers (1)

Riccardo Scorretti
Riccardo Scorretti on 7 Apr 2022
Edited: Riccardo Scorretti on 7 Apr 2022
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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