Limit it all!

$f(n)=\lim _{ n\rightarrow \infty }{ \{ } { (\sqrt { 2 } +1) }^{ n }\} .{ (-1) }^{ [{ (\sqrt { 2 } +1) }^{ n }] }$
Here $n$ is an integer and $[.]$ denotes ' greatest integer function ' and {.} denotes ' fractional part function '.
Find the value of $|f(200)+f(311)+f(434)+f(507)|-f(3)$ .