作业帮1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)…………1/(a+2009)(a+2010)
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1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)…………1/(a+2009)(a+2010)
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)…………1/(a+2009)(a+2010)
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)…………1/(a+2009)(a+2010)
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)…………1/(a+2009)(a+2010)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)…………1/(a+2009)-1/(a+2010)
中间正负抵消
=1/a-1/(a+2010)
=2010/(a²+2010a)
裂项求和....
原式：=[1/a]-[1/a+1]+[1/a+1]-[1/a+2].....+[1/a+2009]-[1/a+2010]
=[1/a]-[1/a+2010]
=2010/[a(a+2010)]
[1/a(a+1)]+[1/(a+1)(a+2)]+[1/(a+2)(a+3)]......+[1/(a+2009)(a+2010)]
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+......+1/(a+2009)-1/(a+2010)
=1/a-1/(a+2010)
=2010/[a(a+2010)]
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