The term independent of x in the expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10, x1, is equ…

Question

The term independent of $x$ in the expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}ight)^{10}$, $x
e1$, is equal to

Answer: 210

Accepted Answer

As in Question 31: this simplifies to $\left(x^{1/3}-x^{-1/2}\right)^{10}$.

$$T_{r+1}=\binom{10}{r}(x^{1/3})^{10-r}(-x^{-1/2})^r$$

Independent of $x$: $\dfrac{10-r}{3}-\dfrac r2=0\Rightarrow20-2r-3r=0\Rightarrow r=4$

$$T_5=\binom{10}{4}=210$$

Solutions · 1