Question

Cho S = \(\dfrac{1}{2}\). \(\dfrac{3}{4}\). \(\dfrac{5}{6}\). ... . \(\dfrac{9999}{10000}\)so sánh S với 0,01

Answer 1

Giải:

Vì:

\(\dfrac{1}{2}< \dfrac{2}{3}.\)

\(\dfrac{2}{3}< \dfrac{3}{4}.\)

.............

\(\dfrac{9999}{10000}< \dfrac{10000}{10001}.\)

\(\Rightarrow S^2< \dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{9999}{10000}.\dfrac{10000}{10001}.\)

\(\Rightarrow S^2< \dfrac{1}{10001}< \dfrac{1}{10000}=\left(\dfrac{1}{100}\right)^2.\)

Mà \(\left(\dfrac{1}{100}\right)^2=0,01^2.\)

\(\Rightarrow S^2< 0,01^2\left(=\left(\dfrac{1}{100}\right)^2\right).\)

\(\Rightarrow S< 0,01.\)

Vậy \(S< 0,01.\)

~ Học tốt!!! ~