Question

[Phạm Trang]

1) so sánh hai phân số sau :

a) \(\dfrac{-6}{11}\) và \(\dfrac{-7}{13}\)

b) \(\dfrac{11}{23}\) và \(\dfrac{17}{29}\)

c) \(\dfrac{25}{13}\) và \(\dfrac{31}{19}\)

2)

Cho S = \(\dfrac{3}{1.4}\)+ \(\dfrac{3}{1.7}\)+ ...+\(\dfrac{3}{40.43}\)+ \(\dfrac{3}{43.46}\)

Chứng minh rằng S < 1

Answer 1

[阮草~๖ۣۜDαɾƙ]

2)

S = \(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{43.46}\)

S = 3 . (\(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{43.46}\))

S = 1 . (\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{43.46}\))

S = 1 . (\(1-\dfrac{1}{4}+...+\dfrac{1}{43}-\dfrac{1}{46}\))

S = 1 . (\(1-\dfrac{1}{46}\))

S = 1 . \(\dfrac{45}{46}\)

S = \(\dfrac{45}{46}\)

=> \(\dfrac{45}{46}\) < 1