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Algebra Difficulty 2.1 Junior Find the answer

When (1−1a)6\left ( 1 - \frac{1}{a} \right ) ^6 is expanded the sum of the last three coefficients is:

Pick one

Solution

This is equivalent to (a−1)6a6.\frac{(a-1)^6}{a^6}.
Its expansion has 7 terms, whose coefficients are the same as those of (a−1)6(a-1)^6.
By the Binomial Theorem, the sum of the last three coefficients is
(62)−(61)+(60)=15−6+1=10 (C)\binom{6}{2}-\binom{6}{1}+\binom{6}{0}=15-6+1=\boxed{10 \textbf{ (C)}}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.