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1),1/2+1/6+1/12+1/20+....+1/10100
=1/1X2+1/2X3+1/3X4+1/4X5+....+1/100X101
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...(1/100-1/101)
=1-1/101
=100/101
2)1/1X3+1/3X5+1/5X7+,,,+1/91X93
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+,,,,+1/2(1/91-1/93)
=1/2(1-1/3+1/3-1/5+1/5-1/7+....+1/91-/93)
=1/2(1-1/93)
=1/2x92/93
=46/93
=1/1X2+1/2X3+1/3X4+1/4X5+....+1/100X101
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...(1/100-1/101)
=1-1/101
=100/101
2)1/1X3+1/3X5+1/5X7+,,,+1/91X93
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+,,,,+1/2(1/91-1/93)
=1/2(1-1/3+1/3-1/5+1/5-1/7+....+1/91-/93)
=1/2(1-1/93)
=1/2x92/93
=46/93
追问
是1/2+1/6+1/12+1/20+1/30+•••+1/900
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