1/31+1/32+1/33+…+1/60. CMR: A< 5 /6

1 bình luận về “1/31+1/32+1/33+…+1/60. CMR: A< 5 /6”

1. A=1/31+1/32+1/33+…+1/60

   =(1/31+1/32+…+1/40)+(1/41+1/42+…+1/50)+(1/51+1/52+…+1/60) ( Mỗi phần trong ngoặc gồm 10 số hạng )

   Nhận xét:
   +)1/31<1/30

   1/32<1/30

   …

   1/40<1/30

   =>1/31+1/32+…+1/40<1/30+1/30+…+1/30=1/30 .10=1/3

   +)1/41<1/40

   1/42<1/40

   …

   1/50<1/40

   =>1/41+1/42+…+1/50<1/40+1/40+…+1/40=1/40 .10=1/4

   +)1/51<1/50

   1/52<1/50

   …

   1/60<1/50

   =>1/51+1/52+…+1/60<1/50+1/50+…+1/50=1/50 .10=1/5

   Từ đó suy ra A<1/3+1/4+1/5=47/60<50/60=5/6

   Vậy A<5/6(Q.E.D)

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