Question

\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+.....+\(\dfrac{1}{9.10}\)<1

Answer 1

giải hộ mình bài này với bạn

 

Answer 2

\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+...+\(\dfrac{1}{9.10}\)< 1

Ta có:

\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+...+\(\dfrac{1}{9.10}\) 

= 1 - \(\dfrac{1}{2}\)+\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+...+\(\dfrac{1}{9}\) - \(\dfrac{1}{10}\) 

 =1 - \(\dfrac{1}{10}\)

 =\(\dfrac{9}{10}\)

=>\(\dfrac{9}{10}\) < 1

Vậy \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+...+\(\dfrac{1}{9.10}\) < 1