Calc. 2 Question, Approximating least integer n
assume that f is the given function. Find the least integer n for which Pn(0.3) approximates ln (1.3)to withinhttps://assessment.casa.uh.edu/Asses...es/2302284.gif
f(x) = ln(1+x)
I'm pretty lost on this problem, I don't really know where to start but I'll write what I have so far...
So ln(1+x) in summation form is (-1)^(n+1) x^n / n
The remainder form which I'm not really sure if I need or not is f^(n+1) (c) x^(n+1) / (n+1)!
I assume we need to use < 1/10000 and find the value of n but I'm not sure how to get to there. The answer is 6... Would appreciate any help!
Re: Calc. 2 Question, Approximating least integer n
Hint: Since it's an alternating series, if you truncate the series after n terms, then the absolute value of the error is never any more than the "n+1"th term.