Question

1-\(\dfrac{1}{1.2}\)-\(\dfrac{1}{2.3}\)-...-\(\dfrac{1}{9.10}\)<\(\dfrac{1}{9}\)

Answer 1

\(1-\dfrac{1}{1.2}-\dfrac{1}{2.3}-...-\dfrac{1}{9.10}\\ =1-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right)\\ =1-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =1-\left(1-\dfrac{1}{10}\right)\\ =1-\dfrac{9}{10}\\ =\dfrac{1}{10}\\ Vì\dfrac{1}{10}< \dfrac{1}{9}\\ Vậy1-\dfrac{1}{1.2}-\dfrac{1}{2.3}-...-\dfrac{1}{9.10}< \dfrac{1}{9}\)

Answer 2

=1-(1-1/2+1/2-1/3+...+1/9-1/10)

=1-1+1/10

=1/10<1/9