展开全部
=(1-1/2)+(1-1/6)+.........+(1-1/240)
=1+......+1-(1/2+1/6+.......1/240)
=1+....+1-(1-1/2+1/2-1/3+1/3-1/4+......-1/15+1/15-1/16)
=15-15/16
=14*(1/16)
=1+......+1-(1/2+1/6+.......1/240)
=1+....+1-(1-1/2+1/2-1/3+1/3-1/4+......-1/15+1/15-1/16)
=15-15/16
=14*(1/16)
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展开全部
1/2 + 5/6 + 11/12 +……+ 239/240
= (1 - 1/2) + (1 - 1/6) + (1 - 1/12) +……+ (1 - 1/240)
= [1 - 1/(1X2)] + [1 - 1/(2X3)] + [1 - 1/(3X4)] +……+ [1 - 1/(15X16)]
= 15- [ 1/(1X2) + 1/(2X3) + 1/(3X4) +……+ 1/(15X16) ]
= 15 - [ (2 -1)/2 + (3 -2)/(2X3) + (4 -3)/(3X4) +……+ (16-15)/(15X16) ]
= 15 - [ 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +……+ 1/914- 1/15 + 1/15 - 1/16 ]
= 15 - [ 1 - 1/16]
= 15 - 1 + 1/16
= 14+ 1/16
= (1 - 1/2) + (1 - 1/6) + (1 - 1/12) +……+ (1 - 1/240)
= [1 - 1/(1X2)] + [1 - 1/(2X3)] + [1 - 1/(3X4)] +……+ [1 - 1/(15X16)]
= 15- [ 1/(1X2) + 1/(2X3) + 1/(3X4) +……+ 1/(15X16) ]
= 15 - [ (2 -1)/2 + (3 -2)/(2X3) + (4 -3)/(3X4) +……+ (16-15)/(15X16) ]
= 15 - [ 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +……+ 1/914- 1/15 + 1/15 - 1/16 ]
= 15 - [ 1 - 1/16]
= 15 - 1 + 1/16
= 14+ 1/16
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谢谢
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