# Thread: Finding Taylor's formula

1. ## Finding Taylor's formula

What's the Taylor's series of $\displaystyle (a^2+\epsilon)^{\frac{1}{n}}$? Using this expansion, what's the value of $\displaystyle (.98)^{\frac{1}{3}}$ accurate to 3 figures beyond the decimal point?

I tried expanding the series for $\displaystyle x^{\frac{2}{n}$ in powers of $\displaystyle \epsilon$ at $\displaystyle x=1$ but my answer seems to be off by .6% with the first 3 terms and appears to get worse when I added more.

2. You should use the Binomial Expansion...

3. I could, but I want to try using Taylor's series to get a hang of it.

4. Which is your independent variable?

5. a. I compared the terms in binomial expansion with my version of Taylor's series for $\displaystyle x^{\frac{2}{n}}$ in powers of $\displaystyle \epsilon$ when x=1 and there appears to be a descrepancy in the coefficients. FYI, the answer through binomial expansion is close to the one I got with a calculator.

6. ok. now the coefficients seems to match if I get a Taylor's series of $\displaystyle x^{\frac{1}{n}$ instead. what gives?

7. ok. seems I got thrown off by $\displaystyle a^2$. should have started with $\displaystyle f(x)=(x+\epsilon)^{\frac{1}{n}}; x=a^2$ and expanded $\displaystyle x^{\frac{1}{n}}$.