1/a(a-1) = 1/(a-1) - 1/a
1/(a-1)(a-2) = 1/(a-2)- 1/(a-1)
...
1/(a-2012)(a-2013) = 1/(a-2013) - 1/(a-2012)
所以
1/a(a-1)+1/(a-1)(a-2)+1/(a-2)(a-3)+……+1/(a-2012)(a-2013)
= 1/(a-2013) - 1/a
请采纳第一个回答正确的人,
1/a(a-1) = 1/(a-1) - 1/a
1/(a-1)(a-2) = 1/(a-2)- 1/(a-1)
...
1/(a-2012)(a-2013) = 1/(a-2013) - 1/(a-2012)
所以
1/a(a-1)+1/(a-1)(a-2)+1/(a-2)(a-3)+……+1/(a-2012)(a-2013)
= 1/(a-2013) - 1/a
请采纳第一个回答正确的人,