I was reading some paper and I got some Taylor series expansion. I was trying to repeat the process but I can not get same result as the paper:
$\sqrt{1 \pm \frac{1}{n}} = 1 \pm \frac{1}{2n} – \frac{1}{8n^2} + O(\frac{1}{n^3})$
Could someone help me to derive it?
Original paper, 10 equation:
Edit: I know how to calculate Taylor series, but in particular situation I got lost.
Best Answer
Hint: Use $$\left(1+a\right)^k=1+ka+\dfrac{k(k-1)}{2}a^2+\dfrac{k(k-1)(k-2)}{2\times3}a^3+\cdots$$ with $a=\pm\frac1n$ and $k=\frac12$.
Edit: changed n to k to mach provided hint and a problem.