Question

[hoang thi hanh]

chứng minh rằng :

12 / 1.4.7  +12 / 4.7.10  +12 / 7.10.12  +...+12 / 54.57.60  <1/2

nhanh đúng like 

Answer 1

[Ngô Văn Nam]

P = 2*[ 6/(1*4*7) + 6/(4*7*10) + ... + 6/(54*57*60) ]
   = 2*[ 1/(1*4) - 1/(4*7) + 1/(4*7) - 1/(7*10) + ... + 1/(54*57) -1/(57*60) ]
   = 2*[ 1/(1*4) - 1/(57*60) ]
   = 2* (427/1710)
   = 427/855 <1/2
S = 1+ 1/2^2 + 1/3^2 +... + 1/100^2
1/2^2 < 1/(1*2)
1/3^2 < 1/(2*3)
...
1/100^2 < 1/(99*100)
==> 1/2^2 +1/3^2 +.., +1/100^2 < 1/(1*2) + 1/(2*3) + ... + 1/(99*100) = 1 -1/2 +1/2 - 1/3 +1/3 -1/4 +... - 1/100
                                                                                                   =1 - 1/100 <1
==> 1/2^2 + 1/3^2 +... + 1/100^2  < 1
==> 1 + 1/2^2 + 1/3^2 +... +1/100^2 <2