E-PA04 · Equality does not justify division by zero
Consider \(F(x)=(1+kx)^n\), where \(n\ge3\) is an integer and k is real.
The coefficients of \(x^2\) and \(x^3\) are equal. Show that either \(k=0\) or \(\displaystyle k=\frac3{n-2}\).
The two equal coefficients are both 7. Find n and k.
Find the coefficient of \(x^4\) in this expansion.
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