The question is: If f(x) = e^x is expanded in its Taylor series, what is the minimum number of terms that must be used to ensure that the resulting polynomial will approximate e^(1/5) to within 10^-6. They say that the answer is 5.
I agree with their reasoning that (f^6(c)(1/5)^6/6!) < 10^-6 and that 5 doesnt work there. So we need to expand the Taylo series until it includes x^5, making it 1+x+x^2/2+x^3/3!+x^4/4!+x^5/5!. But that polynomial has 6 terms, so the minimum number of terms should be 6. I understand that in his notation this polynomial is P5, but P5 has 6 terms! Have I gotten something wrong here?