若f(x+y)=f(x)•f(y),且f(1)=

难度:简单 题型:填空题 来源:不详

题目

若f(x+y)=f(x)•f(y),且f(1)=1,则

f(2)
f(1)
+
f(4)
f(3)
+…+
f(2010)
f(2009)
+
f(2012)
f(2011)
=______.

答案

∵f(x+y)=f(x)•f(y),f(1)=1,
令y=1,则f(x+1)=f(x)•f(1),

f(x+1)
f(x)
=f(1)=1,
f(2)
f(1)
+
f(4)
f(3)
+…+
f(2010)
f(2009)
+
f(2012)
f(2011)
=1006
故答案为:1006

解析

闽ICP备2021017268号-8