If \( a_{0}, a_{1}, a_{2}, \ldots \) are the coefficients in the expansion of \( \left(1+x+x^{2}...
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0If \( a_{0}, a_{1}, a_{2}, \ldots \) are the coefficients in the expansion of \( \left(1+x+x^{2}\right)^{n} \) in ascending powers of \( x \), prove that
\( a_{0} a_{1}-a_{1} a_{2}+a_{2} a_{3}-\ldots=0 \)
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