gaokao 2018 Q12

gaokao · China · national-II-arts 5 marks Sequences and Series Evaluation of a Finite or Infinite Sum
Let $f ( x )$ be an odd function with domain $( - \infty , + \infty )$, satisfying $f ( 1 - x ) = f ( 1 + x )$ and $f ( 1 ) = 2$. Then $f ( 1 ) + f ( 2 ) + f ( 3 ) + \cdots + f ( 50 ) =$
A. $- 50$
B. $0$
C. $2$
D. $50$
Let $f ( x )$ be an odd function with domain $( - \infty , + \infty )$, satisfying $f ( 1 - x ) = f ( 1 + x )$ and $f ( 1 ) = 2$. Then $f ( 1 ) + f ( 2 ) + f ( 3 ) + \cdots + f ( 50 ) =$\\
A. $- 50$\\
B. $0$\\
C. $2$\\
D. $50$