给出下列三个不等试：f(xy)=f(x)+f(y),f(x+y)=f(x)f(y),,f(x+y)=f(x)+f(y)/1-f(x)f(y),
\u5b9a\u4e49\u5728(-1,1)\u4e0a\u7684\u51fd\u6570f(x)-f(y)=f((x-y)/(1-xy)),\u5e76\u4e14f(1/(2011+x))=\u4ee4y=x\uff0c\u5219\u6709f\uff08x\uff09-f\uff08x\uff09=f(0)\uff0c\u5f97f(0)=0
\u4ee4x=0\uff0c\u5219\u6709f(0)-f(y)=f(-y),\u5f97f(-y)=f(y)\u3002\u4e8e\u662ff(x)\u4e3a\u5947\u51fd\u6570
\u75281/x\uff0c1/y\u4ee3\u6362x\uff0cy\uff0c\u5219\u6709f(1/x)-f(1/y)=f[(y-x)/(xy-1)]=f[(x-y)/(1-xy)]=f(x)-f(y)
\u5f97f(x)-f(y)=f(1/x)-f(1/y)
f[1/(2011+x)]=1+f(1/x)
f[1/(2011+x)]-f(1/x)=1
\u4e8e\u662ff(2011+x)-f(x)=1
f[1/(r²+r-1)]=f{[r-(r+1)]/[1-r(r+1)]}=f(r)-f(r+1)
\u4e8e\u662ff(1/5)=f(2)-f(3),f(11)=f(3)-f(4),\u2026\u2026,f[1/(2012²+2012-1)]=f(2012)-f(2013)
\u4e8e\u662fp=f(2)-f(2013)=f(2)-f(2011+2)=-1
\u89e3\uff1a\uff081\uff09\u22351+xn²\u22652\u2502xn\u2502
\u2234\u25022xn/(1+xn²\u2502\u22641 \u53c8x1=1/2
\u2234 \u25022xn/(1+xn²\u2502\uff1c1 f(x1)=f(1/2)=-1
\u800cf(x(n+1)),f(x(n+1))=f(2xn/(1+xn²²)=f[(xn+xn)/(1+xnxn)=f(xn)+f(xn)=2f(xn)
\u2234f(x(n+1))/f(xn)=2 \u2234\ufe5bf(xn)\ufe5c\u662f\u4ee5-1\u4e3a\u9996\u9879\uff0c\u4ee52\u4e3a\u516c\u6bd4\u7684\u7b49\u6bd4\u6570\u5217\uff0c\u6545f(n)=-2^(n-1)
\uff082\uff09\u7531\u9898\u8bbe\uff0c\u6709f\uff080\uff09+f(0)=f[(0+0)/(1+0)]=f(0),\u6545f(0)=0
\u53c8x\u2208(-1,1),\u6709f(x)+f(-x)=f[(x-x)/91-x²]]=f(0)=0
\u5f97f(-x)=-f(x),\u6545\u77e5f(x)\u5728\ufe59-1,1)\u4e0a\u4e3a\u5947\u51fd\u6570. \u7531
1/(k²+3k+1)=1/[ (k+1)(k+2)-1]
=1/(k+1)\uff08k+2\uff09/[1-1/(k+1 )(k+2)
=[1/(k+1)-1/(k+2)]/[1-1/(k+1)(k+2)]
\u5f97f[1/(k²+3k+1)]=f[1/(k+1)+f[-1/(k+2)]=f[1/(k+1)]-f[1/(k+2)]\u2026.
\u4e8e\u662ff[1/(k²+3k+1) ]\u6c42\u548c=f(1/2)-f(1/(n+2))=-1-f\uff081/\uff08n+2\uff09\uff09
\u22341+f(1/5)+f(1/11)+..+f(1/(n²+3n+1)+f(1/(n+2))=0
\u9f99\u8005\u8f7b\u541f\u4e3a\u60a8\u89e3\u60d1,\u51e4\u8005\u8f7b\u821e\u95fb\u60a8\u8ffd\u95ee.
\u5982\u82e5\u6ee1\u610f,\u8bf7\u70b9\u51fb[\u6ee1\u610f\u7b54\u6848];\u5982\u82e5\u60a8\u6709\u4e0d\u6ee1\u610f\u4e4b\u5904,\u8bf7\u6307\u51fa,\u6211\u4e00\u5b9a\u6539\u6b63!
\u5e0c\u671b\u8fd8\u60a8\u4e00\u4e2a\u6b63\u786e\u7b54\u590d!
\u795d\u60a8\u5b66\u4e1a\u8fdb\u6b65!
f(x)=3^x满足f(x+y)=f(x)f(y)
f(x)=log2x 满足f(xy)=f(x)+f(y)
f(x)=tanx 满足f(x+y)=f(x)+f(y)/1-f(x)f(y)
sinx
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