Question

chứng tỏ rằng

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}< 1\)

Answer 1

giúp mình nhé

Answer 2

Đặt :

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+................+\dfrac{1}{99.100}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+............+\dfrac{1}{99}-\dfrac{1}{100}\)

\(A=1-\dfrac{1}{100}\)

\(A=\dfrac{99}{100}< 1\)

\(\Rightarrow A< 1\)

\(\Rightarrow\dfrac{1}{1.2}+\dfrac{1}{2.3}+.........+\dfrac{1}{99.100}< 1\rightarrowđpcm\)