(1X4+2)(3X6+2)(5X8+2)...(2001X2004+2)/(2X5+2)(4X7+2)(6X9+2)...(2002X2005+2) /是除号...矿号之间乘...
问题描述：
(1X4+2)(3X6+2)(5X8+2)...(2001X2004+2)/(2X5+2)(4X7+2)(6X9+2)...(2002X2005+2) /是除号...矿号之间乘...
答
分子上第n项:n(n+3)+2=n^2+3n+2=(n+1)(n+2)
分母上第n项:(n+1)(n+4)+2=n^2+5n+6=(n+2)(n+3)
将上述两个结果带入原式,得到：
原式=(2/4)(3/5)(4/6)……[(n+1)/(n+3)]
=(2X3)/[(n+2)(n+3)]
=6/(n^2+5n+6)
懂了吗? 祝你成功!