How many term of the MAclaurin series for ln(1+x) do you need to use to estimate ln(1.4) to within 0.001?
I have tried this 10 different ways and I keep getting bigger values.
The MacLaurin series is:
For the alternating series, if we stop the interation after the summing of the term , the [obvious] error criterion is...
(1)
Computing the 'infinite sum'...
(2)
... the condition is met for n= 5, i.e. five term of (2) are enough and that gives...
(3)
The 'exact' value is...
(4)
Kind regards
The series expansion...
(1)
... converges in genearal for complex values of z if |z|<1. It is interesting the computation of (1) for . Summing 'only' 44 complex terms of (1) we obtain...
... where both real and imaginary part have an error less than ...
Kind regards