Hello everyone I am a student in high school and I have a question how can I calculate this expression: $\binom{6n}{0}-\binom{6n}{3}+\binom{6n}{6}-\binom{6n}{9}+\cdots +\binom{6n}{6n}$ ?
2026-03-28 00:46:44.1774658804
Calculating a Binomial Expression
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Hint:
Consider $(1-x)^{6n}$. Put in $x=1,\omega,\omega^2$ where $\omega =\exp(i2\pi/3)$, add the expressions and divide by $3$.