Question

Number of terms in the expansion of ${\left[\right(x+\frac{1}{x}{)}^2-(x-\frac{1}{x}{)}^2]}^{1007}$ is ...

• A. $2013$
• B. $2014$
• C. $1$
• D. $2008$

Answer 1

The correct option is C $1$

${[{(x+\frac{1}{x})}^2-{(x+\frac{1}{x})}^2]}^{1007}$

$\Rightarrow {[x^2+\frac{1}{x^2}+2-(x^2+\frac{1}{x^2}-2)]}^{1007}$

$\Rightarrow {(x^2+\frac{1}{x^2}-x^2-\frac{1}{x^2}+2+2)}^{1007}$

$x^2+\frac{1}{x^2}{4}^{1007}$

$x^2+\frac{1}{x^2}$ No. of term $:1$ Option $C$ is correct