вычислите 1/1х2+1/2х3+1/3х4+...+1/2009х2010. ..+1/2009х2010.

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1/(1*2)+1/(2*3)+...+1/(2009*2010) =
(1/1 - 1/2)+(1/2 - 1/3)+...+(1/2009 - 1/2010) =
1 - 1/2 + 1/2 - 1/3 + 1/3 -..-1/2009 + 1/2009 - 1/2010 =
1 - 1/2010 =
2009/2010