求1\1X2+1\2X3+1\3X4+1\4X5.+1\2009X2010的值,请帮我解答,抱歉,刚才那道题写错了,应该是1\1X2+1\2X3+1\4X5+1\6X7+...1\2009X2010,实在是sorry,

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求1\1X2+1\2X3+1\3X4+1\4X5.+1\2009X2010的值,请帮我解答,抱歉,刚才那道题写错了,应该是1\1X2+1\2X3+1\4X5+1\6X7+...1\2009X2010,实在是sorry,
求1\1X2+1\2X3+1\3X4+1\4X5.+1\2009X2010的值,请帮我解答,
抱歉,刚才那道题写错了,应该是1\1X2+1\2X3+1\4X5+1\6X7+...1\2009X2010,实在是sorry,

求1\1X2+1\2X3+1\3X4+1\4X5.+1\2009X2010的值,请帮我解答,抱歉,刚才那道题写错了,应该是1\1X2+1\2X3+1\4X5+1\6X7+...1\2009X2010,实在是sorry,
1\1X2+1\2X3+1\3X4+1\4X5.+1\2009X2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010

这个很简单的。拆开后就是1-1/2+1/2-1/3+1/3+...+1/2009-1/2010 最后抵消了就是2009/2010

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+-------------------+(1/2009-1/2010)
=1-1/2010=2009/2010

1-1/2+1/2-1/3+1/3-1/4······+1/2009-1/2010=1-1/2010=2009/2010

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