求/1/2-1/+/1/3-1/2/+/1/4-1/3/+/1/5-1/4/+···+/1/10-1/9/的值
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![求/1/2-1/+/1/3-1/2/+/1/4-1/3/+/1/5-1/4/+···+/1/10-1/9/的值](/uploads/image/z/9327878-62-8.jpg?t=%E6%B1%82%2F1%2F2-1%2F%2B%2F1%2F3-1%2F2%2F%2B%2F1%2F4-1%2F3%2F%2B%2F1%2F5-1%2F4%2F%2B%C2%B7%C2%B7%C2%B7%2B%2F1%2F10-1%2F9%2F%E7%9A%84%E5%80%BC)
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求/1/2-1/+/1/3-1/2/+/1/4-1/3/+/1/5-1/4/+···+/1/10-1/9/的值
求/1/2-1/+/1/3-1/2/+/1/4-1/3/+/1/5-1/4/+···+/1/10-1/9/的值
求/1/2-1/+/1/3-1/2/+/1/4-1/3/+/1/5-1/4/+···+/1/10-1/9/的值
因为1/2-1﹤0, 1/3-1/2﹤0, 1/4-1/3﹤0, 1/5-1/4﹤0……,1/10-1/9﹤0
所以
原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
=1-1/10
=9/10