Question

Chứng minh rằng: 1/3.4+1/4.5+...+1/19.20<1/2. có lời giải chi tiết

Answer 1

\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{20}=\dfrac{1}{3}-\dfrac{1}{20}=\dfrac{17}{60}< \dfrac{1}{2}\)

Answer 2

\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{19.20}< \dfrac{1}{2}\)

=> \(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{20}< \dfrac{1}{2}\)

=> \(\dfrac{1}{3}-\dfrac{1}{20}< \dfrac{1}{2}\)

Answer 3

\(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+.....+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=\dfrac{1}{3}-\dfrac{1}{20}=\dfrac{17}{60}\)

mà \(\dfrac{17}{60}< \dfrac{1}{2}\)

\(=>\dfrac{1}{3.4}+\dfrac{1}{4.5}+.....+\dfrac{1}{19.20}< \dfrac{1}{2}\)