power series

**alexandrabel90** · October 24th 2010, 02:04 PM

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

**Dinkydoe** · October 24th 2010, 02:17 PM

http://en.wikipedia.org/wiki/Radius_of_convergence

eh no.... $R=\lim_{n\to\infty}|(a_n/a_{n+1})|= \lim_{n\to\infty}(n+1)=\infty$

**alexandrabel90** · October 24th 2010, 02:18 PM

are you sure?

**Dinkydoe** · October 24th 2010, 02:19 PM

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.

**alexandrabel90** · October 24th 2010, 02:22 PM

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

**Plato** · October 24th 2010, 02:30 PM

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

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

**alexandrabel90** · October 24th 2010, 02:32 PM

infinity(:

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