# Thread: Taylor series at a point

1. ## Taylor series at a point

hey can someone help me get the solution for this problem thanks

The Taylor series for e^x at point x=0 is given by

e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + (x^5)/5! + ....

what is the truncation (true) error in the representation of e^1 if only four terms of the series are used?

2. Originally Posted by Eng
hey can someone help me get the solution for this problem thanks

The Taylor series for e^x at point x=0 is given by

e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + (x^5)/5! + ....

what is the truncation (true) error in the representation of e^1 if only four terms of the series are used?
$e \approx 1 + 1 + \frac{1}{2} + \frac{1}{6}
$

true error will be, $e - (the \, \, approximation)$