Question

已知奇函數(shù)f(x)的定義域為R,且是以2為周期的周期函數(shù),數(shù)列{a_n}是首項為1,公差為1的等差數(shù)列,則f(a₁)+f(a₂)+…+f(a₁₀)的值為

A.0               B.1                C.-1                    D.2

Answer 1

解析：a_n=1+n-1=n,又f(x)是定義在R上周期為2的周期函數(shù),

∴f(2)=f(0)=0,f(3)=f(1)=f(-1)=-f(1).

∴f(1)=0,即f(n)=f(a_n)=0.

∴f(a₁)+f(a₂)+…+f(a₁₀)=0.

答案：A