已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x、y属于R),求f(2010)值.
已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x、y属于R),求f(2010)值.
数学人气:416 ℃时间:2019-11-16 00:50:54
优质解答
4 f (0) f (0) = 2 f (0)f (0) = 1/24 f (0) f (x) = f (x) + f (x) = 2 f (x)4 f (x) f (1) = f (x + 1) + f (x - 1)f (x + 1) = f (x) - f (x - 1)f (x) = f (x - 1) - f (x - 2)事实上可以求得通项公式(1/4)*(1/2...
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