问题 解答题
若f(a+b)=f(a)•f(b)且f(1)=2.则
f(2)
f(1)
+
f(3)
f(2)
+…+
f(2012)
f(2011)
=______.
答案

令b=1.∴f(a+1)=f(a)f(1)

f(a+1)
f(a)
=f(1)=2

f(2)
f(1)
=2.
f(3)
f(2)
=2.…
f(2012)
f(2011)
=2

f(2)
f(1)
+
f(3)
f(2)
+…+
f(2012)
f(2011)
=2011×2=4022.答案:4022.

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