Find the constant term in the expansion of $\Big(x^2+\frac{1}{x}\Big)^4$.

Blizzardshine Jun 8, 2022

#1**+2 **

I'm not sure if this even has a constant term. Also please write in LaTeX so it is easy for anyone to understand.

**-Vinculum**

Vinculum Jun 8, 2022

#2**+1 **

normally I would not answer a question presented like this either.

But

I am curious to see what this looked like, I have not seen the big command before.

\(\Big(x^2+\frac{1}{x}\Big)^4\)

general term

\(\binom{4}{n}(\frac{1}{x})^n(x^2)^{4-n}\\ =\binom{4}{n}(x)^{-n}(x)^{8-2n}\\ =\binom{4}{n}(x)^{8-3n}\\\)

n must be 0,1,2,3 or 4 so 8-3n cannot be zero

Hence there is no constant term.

Melody Jun 17, 2022