Giúp mình với!( Mình ko pit' đánh phân số, thông cảm nha!)

H

hiensau99

[TEX]\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+,,,,+\frac{99}{100!}[/TEX]

[TEX]=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+,,,,+\frac{100-1}{100!}[/TEX]

[TEX]=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+....+\frac{1}{99!}-\frac{1}{100!}[/TEX]

[TEX]=1-\frac{1}{100!}[/TEX] < 1 (đpcm)
 
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