E-GT04 · When a constant can exist
Let n be a positive integer and consider \(\displaystyle (x^3+\frac2x)^n\), where \(x\ne0\).
Show that the exponent of x in the general term is \(3n-4r\). State the allowed indices.
For \(1\le n\le12\), find every n for which there is a nonzero constant term, and find each constant term.
For the smallest n found, expand completely. Explain why there is no term in \(x^3\).
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