- #1
Justabeginner
- 309
- 1
Homework Statement
Use x=-1/2 in the MacLaurin series for e^x to approximate 1/sqrt(e) to four decimal places.
Homework Equations
The Attempt at a Solution
[itex] \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + x^2/2 + x^3/6 + ... [/itex]
For this particular power series, I have:
[itex] \sum_{n=0}^\infty \frac{(x+0.5)^n}{sqrt(e)(n!)} = 1/sqrt(e) + (x+0.5)/(sqrt(e)) + (x+0.5)^2/sqrt(e) + (x+0.5)^3/6*sqrt(e)... [/itex]
(-1/2)^(n+1)/(n+1)! <= 0.00004
n= 2
(1/sqrt(e) + (x+0.5)/sqrt(e) + (x+0.5)^(2)/2*sqrt(e)) = (1/sqrt(e) + 0 + 0)= 1/sqrt(e)= 0.6065
But this doesn't seem right because I should end up with the actual number instead of the 1/sqrt(e) itself. I thought I was doing the method correctly, but I guess not. I would appreciate any insight on this at all, as I don't know of any other method to apply here. Thanks!