Cho \(S = + + + ... + Chọn câu đúng.

* Hướng dẫn giải

  \(S = \dfrac{1}{{21}} + \dfrac{1}{{22}} + \dfrac{1}{{23}} + ... + \dfrac{1}{{35}}\)

\(S = \left( {\dfrac{1}{{21}} + ... + \dfrac{1}{{25}}} \right) + \left( {\dfrac{1}{{26}} + ... + \dfrac{1}{{30}}} \right) + \left( {\dfrac{1}{{31}} + ... + \dfrac{1}{{35}}} \right)\)

\(S > \left( {\dfrac{1}{{25}} + ... + \dfrac{1}{{25}}} \right) + \left( {\dfrac{1}{{30}} + ... + \dfrac{1}{{30}}} \right) + \left( {\dfrac{1}{{35}} + ... + \dfrac{1}{{35}}} \right)\)

\(S > \dfrac{1}{5} + \dfrac{1}{6} + \dfrac{1}{7} = \dfrac{{107}}{{210}} > \dfrac{1}{2}\)

Vậy \(S > \dfrac{1}{2}\)