Question

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

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

Answer 1

Answer: (A)

We have, $T_r={}^{2r}{C}_{r-1}{\left(x\right)}^{2r-r+1}{\left(\frac{1}{x}\right)}^{r-1}$
$=\frac{\lfloor 2r}{\lfloor r-1\lfloor r+1}{x}^{r+1-r+1}$
$=\frac{\lfloor 2r}{\lfloor r-1\lfloor r+1}{x}^2$