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)](/uploads/image/z/6527912-32-2.jpg?t=1%2Fa%28a%2B1%29%2B1%2F%28a%2B1%29%28a%2B2%29%2B1%2F%28a%2B2%29%28a%2B3+%29%2B%E2%80%A6%E2%80%A6%2B1%2F%28a%2B2009%29%28a%2B2010%29)
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)]
=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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