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harrypham

Ta có [TEX]S= 2 \left( \frac{1}{1.2}+ \frac{1}{2.3}+...+ \frac{1}{n(n+1)} \right)= 2 \left( \frac{2-1}{1.2}+ \frac{3-2}{2.3}+...+ \frac{(n+1)-n}{n(n+1)} \right)= 2 \left( 1- \frac{1}{2}+ \frac{1}{2}- \frac{1}{3}+...+ \frac{1}{n}- \frac{1}{n+1} \right)[/TEX]
[TEX]\Rightarrow S= 2 \left( 1- \frac{1}{n+1} \right)= 2- \frac{2}{n+1}<2[/TEX]
 
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