For positive integer $n$, consider $\left(x^2+\frac1x\right)^n.$ Prove that a constant term exis

Question

For positive integer $n$, consider $\left(x^2+\frac1x\right)^n.$ Prove that a constant term exists if and only if $n$ is divisible by $3$. Give a formula for that constant term when it exists. Find it when $n=12$.

Accepted Answer

(a) $3\mid n$; (b) Constant term $\binom n{\frac{2n}{3}}$; (c) $495$ when $n=12$.

Binomial Theorem

Binomial Theorem

Solution:

Solution locked