Solve the Problem $f ( x , y , z ) = \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x + y ) ^ { 2 n } } { ( 2 n ) ! z ^ { 2 n } }$

Multiple Choice

Solve the problem.
-Find an equation for the level surface of the function $f ( x , y , z ) = \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x + y ) ^ { 2 n } } { ( 2 n ) ! z ^ { 2 n } }$ that passes through the point $( \pi , \pi , 1 )$ .

A) $\cos \left( \frac { x + y } { z } \right) = 0$
B) $\frac { x + y } { z } = 2 \pi$
C) $\cos \left( \frac { x + y } { z } \right) = 2 \pi$
D) $\frac { x + y } { z } = 1$