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簡便計算1+31/6+51/12+71/20+91/30+111/42？

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  • 1 # 指尖時

    1 + 31/6 + 51/12 + 71/20 + 91/30 + 111/42

    = 1 + (30+1)/6 + (48+3)/12 + (60+11)/20 + (90+1)/30 + (84+27)/42

    = 1 + 5+ 1/6 + 4+ 1/4 + 3+ 11/20 + 3+ 1/30 + 2+ 9/14

    = 1 + 5 + 4 + 3 + 3 + 2 + 10/60 + 15/60 + 33/60 + 2/60 + 9/14

    = 18 + 25/60 + 35/60 + 9/14

    = 18 + 60/60 + 9/14

    = 19 + 9/14

    1/(1X4) + 1/(4X7) + 1/(7X10) + …… + 1/(73X76)

    = 3/3 X [ 1/(1X4) + 1/(4X7) + 1/(7X10) + …… + 1/(73X76) ]

    = (1/3) X [ 3/(1X4) + 3/(4X7) + 3/(7X10) + …… + 3/(73X76) ]

    = (1/3) X [ (4-1)/(1X4) + (7-4)/(4X7) + (10-7)/(7X10) + ……+ (76-73)/(73X76) ]

    = (1/3) X [ 4/4 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 + …… - 1/73 + 1/73 - 1/76 ]

    = (1/3) X ( 1 - 1/76 )

    = 1/3 X 75/76

    = 25/76

    8787 8787 X 777 7777 / 1010101 / 111 1111

    = 87878787 / 1010101 X 777 7777 / 111 1111

    = 87 X 7

    = ( 90 - 3 ) X 7

    = 630 - 21

    = 609

    99999 X 22222 + 33333 X 33334

    = 33333 X 66666 + 33333 X 33334

    = 33333 X ( 66666 + 33333 + 1 )

    = 33333 X ( 99999 + 1 )

    = 33333 X 100000

    = 33 3330 0000

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