[toán 8]CM bất đẳng thức

L

linh_tinh_96

đặt vế trái là A
[tex]A[/tex] [tex]<[/tex] [tex]\frac{1}{2^3-2}[/tex] [tex]+[/tex] [tex]\frac{1}{3^3-3}[/tex] [tex]...[/tex] [tex]\frac{1}{n^3-n}[/tex] [tex]=[/tex] [tex]\frac{1}{1.2.3}[/tex] [tex]+[/tex] [tex]\frac{1}{2.3.4}[/tex] [tex]...[/tex] [tex]\frac{1}{(n-1)n(n+1)}[/tex] [tex]=[/tex] [tex]\frac{1}{2}[/tex] [tex][[/tex] [tex]\frac{1}{1*2}[/tex] - [tex]\frac{1}{2.3}[/tex] [tex]...[/tex] [tex]\frac{1}{(n-1)n}[/tex] - [tex]\frac{1}{n(n+1)}[/tex] [tex]][/tex] [tex]=[/tex] [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{2n(n+1)}[/tex] [tex]<[/tex] [tex]\frac{1}{4}[/tex]

=) dpcm
 
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