Taylor Series - Range of values

1. May 18, 2008

wombat4000

1. The problem statement, all variables and given/known data

im being asked for the first 4 non zero values for the taylor expansion of exp(x) which is simple, but then it asks for the range of x values that are valid for the expansion.

i have never come accross ths before - any idea?

2. May 18, 2008

GSpeight

From the first four coefficients of the taylor expansion you can guess what the nth coefficient is going to be. Is there then some test you can use to find out when a sum (don't worry about it being a taylor series!) converges?

3. May 18, 2008

wombat4000

ratio test? integral test?

but how will working out if the sum convereges help with obtaining the valid x values?

4. May 18, 2008

GSpeight

The ratio test is useful for calculating when taylor series converge. Each of the terms of your sum is in terms of 'x' so the ratio test tells you when the sum converges in terms of x.

5. May 18, 2008

wombat4000

the question doesnt mention sum or convergence?

6. May 18, 2008

GSpeight

The taylor series expansion is going to be valid where the sum converges, or alternatively you can just write that the taylor series expansion for exp is valid everywhere if you've been told this fact.