In the following exercise, model the addition.
5+3
In this exercise, find each indicated sum.
âi=1â(â25)iâ1\sum\limits_{i=1}^{\infty}\left(-\frac{2}{5}\right)^{i-1} i=1âââ(â52â)iâ1
Use the result of Earlier Exercise in Earlier Section to show that the Maclaurin series of the function
f(x)={eâ1/x2 for xâ 00 for x=0f(x)= \begin{cases}e^{-1 / x^2} & \text { for } x \neq 0 \\ 0 & \text { for } x=0\end{cases} f(x)={eâ1/x20â for xî =0 for x=0â
is T(x)=0. This provides an example of a function f whose Maclaurin series converges but does not converge to f(x) (except at x=0 ).
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