Question

So sánh: 1/100+1/101+1/102+...+1/200 và 0,499

Answer 1

Ta xét: \(\dfrac{1}{100} + \dfrac{1}{101} + \dfrac{1}{102}...+ \dfrac{1}{200}\)

\(\dfrac{1}{100} > \dfrac{1}{200}\)

\(\dfrac{1}{101}>\dfrac{1}{200}\)

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\(\dfrac{1}{199}>\dfrac{1}{200}\)

\(\Rightarrow\)\(\dfrac{1}{100} + \dfrac{1}{101} + \dfrac{1}{102} +...+\dfrac{1}{200}\)(có 101 phân số) > \(100.\dfrac{1}{200} = \dfrac{1}{2}\)

Answer 2

Lời giải:
\(\frac{1}{100}+\frac{1}{101}+...+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+....+\frac{1}{200}=\frac{101}{200}>\frac{100}{200}=0,5>0,499\)