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Given that $\sum _{ n=0 }^{ \infty }{ { a }_{ n } } { x }^{ n }$ is a Taylor series that converges to $f\left( x \right) $ for all real $x$, $f^{ ' }\left( 1 \right) =$

$0$

$\sum _{ n=0 }^{ \infty }{ { a }_{ n } } $

$\sum _{ n=0 }^{ \infty }{ { na }_{ n } } $

$\sum _{ n=0 }^{ \infty }{ { a }_{ n } } nx$