1/2-1/6-1/12-1/20-1/30和20-2/3-2/15-2/35-2/63-2/99如何用简便方法计算
展开全部
第一题:
1/2-1/6-1/12-1/20-1/30
=(1-1/2)-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)
=1-1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6
=0+1/6
=1/6
第二题:
20-2/3-2/15-2/35-2/63-2/99
=20-(1-1/3)-(1/3-1/5)-(1/5-1/7)-(1/7-1/9)-(1/9-1/11)
=20-1+1/3-1/3+1/5-1/5+1/7-1/7+1/9-1/9+1/11
=20-1+1/11
=19+1/11
=19又1/11
1/2-1/6-1/12-1/20-1/30
=(1-1/2)-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)
=1-1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6
=0+1/6
=1/6
第二题:
20-2/3-2/15-2/35-2/63-2/99
=20-(1-1/3)-(1/3-1/5)-(1/5-1/7)-(1/7-1/9)-(1/9-1/11)
=20-1+1/3-1/3+1/5-1/5+1/7-1/7+1/9-1/9+1/11
=20-1+1/11
=19+1/11
=19又1/11
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