# Limit it all!

**Calculus**Level 3

\(f(n)=\lim _{ n\rightarrow \infty }{ \{ } { (\sqrt { 2 } +1) }^{ n }\} .{ (-1) }^{ [{ (\sqrt { 2 } +1) }^{ n }] }\)

Here \(n\) is an integer and \([.]\) denotes '**greatest integer function**' and **{.}** denotes '**fractional part function**'.

Find the value of \(|f(200)+f(311)+f(434)+f(507)|-f(3)\).