问题描述:
1/3+1/15+1/35+.........1/1993*1995=?
=997/1995吗?
问题解答:
1/3+1/15+1/35+.........1/1993*1995
=1/1*3+1/3*5+1/5*7+...+1/1993*1995
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/1993-1/1995)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/1993-1/1995)
=1/2(1-1/1995)
=1/2*1994/1995
=997/1995
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