You should use the Binomial Expansion...
What's the Taylor's series of ? Using this expansion, what's the value of accurate to 3 figures beyond the decimal point?
I tried expanding the series for in powers of at but my answer seems to be off by .6% with the first 3 terms and appears to get worse when I added more.
a. I compared the terms in binomial expansion with my version of Taylor's series for in powers of 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.