Question

2/1*2+2/2*3+2/3*4+……+2/2008*2009+2/2009*2010=

Answer 1

2/1*2+2/2*3+2/3*4+……+2/2008*2009+2/2009*2010
这里提取2
原式前冲=2*(1-1/2+1/2-1/3+1/3-1/卖悔咐4++++++1/2009-1/2010)
=2*(1-1/2010)
=2*2009/2010
=2009/1005
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Answer 2

2/1*2+2/2*3+2/3*4+……+2/2008*2009+2/2009*2010
=2*(1/1*2+1/2*3+1/3*4+……1/2008*2009+1/瞎野2009*2010)
=2*[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/梁神胡4-1/5)+......+(1/橡拦2008-1/2009)+(1/2009-1/2010)]
=2*(1-1/2010)
=2*(2009/2010)
=2009/1005