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# Taylor Series for e^x with while loop

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Clare Dubecky on 2 Oct 2020
I am attempting to write a code that will use a while loop to add terms of a taylor series approximation for e^x to a return value called "sum". I am trying to get the while loop to continue until the value of sum does not change after adding a new term. My main question is what term could I use to start the while loop? Should I have it be
while sum(i) ~= sum(i - 1)
end
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James Tursa on 2 Oct 2020
Best to use a different variable name than sum, since sum is a standard MATLAB function. E.g., mysum.
Just give mysum(1) and mysum(2) the first two sums of the Taylor series and start i at 2.
That being said, you will not get good results with this as x gets larger, particularly when negative. The intermediate terms can grow hugely before the factorial in the denominator starts to dominate and the terms settle down. In the meantime you will get large cancellation errors in the intermediate sums.

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### Answers (1)

Sulaymon Eshkabilov on 3 Oct 2020
x = 1.5;
SUM = 0;
ANS = exp(x);
Err = ANS-SUM;
Err_Margin = 1e-9;
ii=0;
while Err > Err_margin
ii=ii+1;
SUM(ii+1) = SUM(ii)+...
ERR = ANS-SUM(ii+1);
end
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