$3^\text{rd}$ of day

Algebra Level 3

Find the coefficient of the term that doesn't have $x$ in the expansion of

$\left(\sqrt[4]{x}+\frac{1}{\sqrt[10]{x}}\right)^7.$

1 solution

Paola Ramírez
Feb 26, 2015

Let $\binom{7}{n} x^{\frac{n}{4}} x^{\frac{7-n}{-10}}$ the term which has no $x$ so $\frac{n}{4}=\frac{7-n}{-10} \Rightarrow n=2$

$\therefore$ the coefficient is $\boxed{\binom{7}{2}=21}$

wahhhhhhh i dont know it

Lesterjohn Casinillo - 6 years, 3 months ago

according to your solution n=2 would give (1/2) + (1/2) for power of x which is 1. which does not remove x.

Faisal Basha - 6 years, 3 months ago

It is corrected, thanks

Paola Ramírez - 6 years, 3 months ago

but 5 should be multiplied to 21. please check.

Rajit Das - 6 years, 3 months ago