Taylor Series Converges to e^-x for All x

[tnutty]

True/false The taylor series below converges for all x to e^-x

n-infinity
\sum (-1)^(n-1) * 1/n * x^n
n=1

 

[SNOOTCHIEBOOCHEE]

well the series for e^x is Sum: x^n/n!

I will assume you forgot to put the factorial in there. Cause then it is obviously falso

So now (-1x)^n/n!= (-1)^n x^n/n! = e^-x

So this is false, it converges to -e^-x

my notaion is very sloppy, but you get the picture

 

[tnutty]

nope did not forgot the factorial. Why is it obviously false then.