# Thread: power series

1. ## power series

i having great problems trying to find the R= radius of convergence.

the qns is. show that R= infinity for the series exp(x) = 1+ x/1! + x^2 /2! +...

my working:

exp (x) = summation from n=0 to infinity (x^n)/n!

i cant think of a way how to make n start from 1 instead of 0.

so in this case, let a_n = 1/n!

then using ratio test, R = lim (a_n+1 / a_n) = 1/(n+1)

thus as n tends to infinity, R tends to 0... but i need to show that R= infinity eh no.... $\displaystyle R=\lim_{n\to\infty}|(a_n/a_{n+1})|= \lim_{n\to\infty}(n+1)=\infty$

3. are you sure?

4. Originally Posted by alexandrabel90 are you sure?
Have you checked the link?

Radius of convergence - Wikipedia, the free encyclopedia

See definition of Radius of convergence.

5. oh! becos my lecture notes wrote it the other way round. guess its a mistake in the notes.

thanks for pointing it out to me

6. The root test gives $\displaystyle \left( {\forall x} \right)\left[ {\dfrac{{\left| x \right|}}{{\sqrt[n]{{n!}}}} \to 0} \right]$.

Because it converges for all $\displaystyle x$, what is the radius of convergence?

7. infinity(:

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