If \( F(x)=\left(1+x^{2}-x^{3}\right)^{1000}=\sum_{k=0}^{3000} a_{k...

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If \( F(x)=\left(1+x^{2}-x^{3}\right)^{1000}=\sum_{k=0}^{3000} a_{k} x^{k} \)
and \( G(x)=\left(1-x^{2}+x^{3}\right)^{1000}=\sum_{k=0}^{3000} b_{k} x^{k} \) then
(a) \( a_{40}b_{40} \)
(b) \( a_{40}=b_{40} \)
(c) \( b_{40}-a_{40}=2^{20} \)
(d) \( a_{40}+b_{40}=2^{40} \)
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