Đáp án+Giải thích các bước giải:
1) S=$\dfrac{1}{31}$+$\dfrac{1}{32}$+....+$\dfrac{1}{60}$
S=($\dfrac{1}{31}$+$\dfrac{1}{32}$+...+$\dfrac{1}{40}$)+($\dfrac{1}{41}$+$\dfrac{1}{42}$+...+$\dfrac{1}{50}$)+($\dfrac{1}{51}$+$\dfrac{1}{52}$+...+$\dfrac{1}{60}$)
⇒ S>($\dfrac{1}{40}$+$\dfrac{1}{50}$+$\dfrac{1}{60}$).10
⇒ S>$\dfrac{1}{4}$+$\dfrac{1}{5}$+$\dfrac{1}{6}$
⇒ S>$\dfrac{3}{5}$
2) S=$\dfrac{1}{31}$+$\dfrac{1}{32}$+....+$\dfrac{1}{60}$
S=($\dfrac{1}{31}$+$\dfrac{1}{32}$+...+$\dfrac{1}{40}$)+($\dfrac{1}{41}$+$\dfrac{1}{42}$+...+$\dfrac{1}{50}$)+($\dfrac{1}{51}$+$\dfrac{1}{52}$+...+$\dfrac{1}{60}$)
⇒ S<($\dfrac{1}{31}$+$\dfrac{1}{41}$+$\dfrac{1}{51}$).10
⇒ S<($\dfrac{1}{30}$+$\dfrac{1}{40}$+$\dfrac{1}{50}$).10
⇒ S<$\dfrac{1}{3}$+$\dfrac{1}{4}$+$\dfrac{1}{5}$<$\dfrac{4}{5}$
⇒ S<$\dfrac{4}{5}$
Vậy $\dfrac{3}{5}$<S<$\dfrac{4}{5}$
