Question

1/3.3+1/4.4+1/5.5...+1/100.100<1/2 ( chứng minh)

Answer 1

\(< \dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(=\dfrac{1}{2}-\dfrac{1}{100}< \dfrac{1}{2}\left(đpcm\right)\)

 

Answer 2

sai đề

 

Answer 3

1/3.3+1/4.4+1/5.5+...+1/100.100<1/2.3+1/3.4+1/4.5+...+1/99.100=A

A=1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100=1/2-1/100<1/2

=>1/3.3+1/4.4+1/5.5+...+1/100.100<1/2