一道简单的数学趣味计算题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)

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一道简单的数学趣味计算题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)一道简单的数学趣味计算题计算1/a(a+1)+1/(a+1)

一道简单的数学趣味计算题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)
一道简单的数学趣味计算题
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)

一道简单的数学趣味计算题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)
1/a(a+1)=1/a-1/(a+1)
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+……+1/(a+2004)(a+2005)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+……+1/(a+2004)-1/(a+2005)
=1/a-1/(a+2005)
=2005/a(a+2005)

1/a-1/(a+2005)

这道题并不难,但是把过程迅速的打到这里来就很难了。谁打字(确切的说是符号)速度快谁就能得分。