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

 Jun 8, 2022
 #1
avatar+579 
+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

 

smileysmileysmiley

 Jun 8, 2022
 #2
avatar+118135 
+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.

 Jun 17, 2022

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