1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.
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![1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.](/uploads/image/z/5550658-34-8.jpg?t=1%2F1x3%2B1%2F3x5%2B1%2F5x7%2B.%2B1%2F1997x1999+%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97.)
1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.
1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.
1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.
1/1x3+1/3x5+1/5x7+.+1/1997x1999
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+.+1/1997-1/1999)
=(1/2)*(1-1/1999)
=999/1999
你好
1/1*3=1/2 * (1-1/3)
1/3*5=1/2 * (1/3-1/5)
所以原式=1/2[(1-1/3)+(1/3-1/5)+……+(1/1997-1/1999)]
=1/2(1-1/1999)
=1/2 * 1998/1999
=999/1999
0.5x(1-1/3+1/3-1/5+......1/1997-1/1999)
1/2(1-1/1999)