\(\dfrac{1}{101}< \dfrac{1}{100}\)
\(\dfrac{1}{102}< \dfrac{1}{100}\)
...
\(\dfrac{1}{200}< \dfrac{1}{100}\)
Do đó: \(\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{200}< \dfrac{1}{100}+\dfrac{1}{100}+...+\dfrac{1}{100}\)
=>\(A< \dfrac{100}{100}=1\)
\(\dfrac{1}{101}>\dfrac{1}{200}\)
\(\dfrac{1}{102}>\dfrac{1}{200}\)
...
\(\dfrac{1}{200}=\dfrac{1}{200}\)
Do đó: \(\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{200}>\dfrac{1}{200}+\dfrac{1}{200}+...+\dfrac{1}{200}\)
=>\(A>\dfrac{100}{200}=\dfrac{1}{2}\)
=>\(\dfrac{1}{2}< A< 1\)
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