For 0 < x < 1, the expansion of \(\left(1+\frac{1}{\text{x}}\right)^{1/2}\) is
1
\(1+\frac{1}{2\text{x}}−\frac{1}{2!}\left(\frac{1}{2\text{x}}\right)^2+\frac{1.3}{3!}\left(\frac{1}{2\text{x}}\right)^3−\frac{1.3 .5}{4!}\left(\frac{1}{2\text{x}}\right)^4+\ldots \ldots\infty\)
2
\(\frac{1}{\sqrt{\text{x}}}+\frac{1}{2}\sqrt{\text{x}}−\frac{1}{2!} \frac{\text{x}\sqrt{\text{x}}}{2^2}+\frac{1.3}{3!} \frac{\text{x}^2\sqrt{\text{x}}}{2^3}−\ldots\ldots\infty\)
3
\(1+\frac{1}{\sqrt{\text{x}}}+\frac{1}{2}\text{x}\sqrt{\text{x}}+\frac{1}{2!} \frac{\text{x}^2 \sqrt{\text{x}}}{2^3}+\frac{1.3}{3!} \frac{\text{x}^3 \sqrt{\text{x}}}{2^4}+\ldots \ldots \infty\)
4
\(\frac{1}{\sqrt{\text{x}}}+\frac{1}{2\text{x}\sqrt{\text{x}}}−\frac{1}{2!}\left(\frac{1}{2\text{x}}\right)^2\frac{1}{\sqrt{\text{x}}}+\frac{1.3}{3!}\left(\frac{1}{2\text{x}}\right)^3 \frac{1}{\sqrt{\text{x}}}−\ldots \ldots \infty\)
5
Not Attempted