infinite series with loop in MATLAB
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hasan s
am 21 Jan. 2021
Kommentiert: hasan s
am 22 Jan. 2021
how can find F in matlab , where the initial value of z =1
and i is loop from
i=1:10
thanks so much for any help.need code of program if possible
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/496158/image.png)
2 Kommentare
David Hill
am 22 Jan. 2021
It is unclear what z array is (from i=1:10) and how i changes in the equation. Should there be another summation on the outside changing i from 1:10?
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Walter Roberson
am 22 Jan. 2021
syms z I k real
F = symsum((-z*I)^k/(k*factorial(k)), k, 1, inf)
However, examine the behavior when k = 0, the lower bound from the equation. The denominator is k*k! which would be 0 * 0! which would be 0*1 which would be 0. So we have a potential problem with singularities, and need to look at the limit. For non-zero z and i, (-z*i)^0 would be 1. Thus we are looking at 1/0 and that is infinite. As that is a term that is included in the actual sum (k = 0 to infinity) we must conclude that F is infinite except for the case where z or i are 0.
12 Kommentare
Walter Roberson
am 22 Jan. 2021
Bearbeitet: Walter Roberson
am 22 Jan. 2021
format long g
z = [1, rand(1,9)];
syms k real
F = sym(0);
for i = 1 : 10
F = F + symsum((-z(i))^k/(k*factorial(k)), k, 1, inf);
end
F
result = double(F)
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