化简1/a(a+10)+1/(a+1)(a+2)+...+1/(a+2009)(a+2010)

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化简1/a(a+10)+1/(a+1)(a+2)+...+1/(a+2009)(a+2010)

化简1/a(a+10)+1/(a+1)(a+2)+...+1/(a+2009)(a+2010)
化简1/a(a+10)+1/(a+1)(a+2)+...+1/(a+2009)(a+2010)

化简1/a(a+10)+1/(a+1)(a+2)+...+1/(a+2009)(a+2010)
题目写错了吧,应该是1/[a(a+1)]+1/[(a+1)(a+2)]+...+1/[(a+2009)(a+2010)]
原式=[(a+1)-a]/[a(a+1)]+[(a+2)-(a+1)]/[(a+1)(a+2)]+...+[(a+2010)-(a+2009)]/[(a+2009)(a+2010)]
=[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)]