16. Starting with the powers series, f x Py n0 xn n! , consider the linear...

16. Starting with the powers series, f ðxÞ ¼

Py n¼0 xn n! , consider the linear approximation f1ðxÞ ¼ 1 þ x. As indicated in (6.33), f ðxÞ  ð1 þ xÞ x2 2

! 1;

as x ! 0. Demonstrate this result by calculating the power series for this ratio function, and confirming that it is absolutely convergent, which then justifies a substitution of x ¼ 0.