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

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

Jun 8, 2022

#1
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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

Jun 8, 2022
#2
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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.

Jun 17, 2022