Question

Find the $r^{th}$ term in the expansion of $\left(x+\frac{1}{x}\right)^{2r}$.

• A. $\frac{\lfloor2r}{\lfloor r-1\lfloor r+1}x^{2}$
• B. $\frac{\lfloor2r}{\lfloor r-1}x$
• C. $\frac{\lfloor2r}{\lfloor r}x^{3}$
• D. None of these

Answer 1

Answer: (A)

We have, $T_{r} = \,{}^{2r}C_{r-1}\left(x\right)^{2r-r+1}\left(\frac{1}{x}\right)^{r-1}$
$=\frac{\lfloor2r}{\lfloor r-1\lfloor r+1}x^{r+1-r+1}$
$= \frac{\lfloor2r}{\lfloor r-1\lfloor r+1}x^{2}$