Question

1. So sanh

a) 42/43 va 58/59

b) 18/31 va 15/37

c) 53/57 va 531/571

d) 25/26 và 25251/26261

e) 3535.232323/353535.2323; 3535/3534 va 2323/2322

g) 13/38 va 1/3

2.Chung minh rang:

a) N=1/4^2+1/6^2+1/8^2+...+1/(2n)^2 < 1/4

b) 1/26+1/27+1/28+...+1/50=1-1/2+1/3-1/4+...+1/49-1/50

c) A=1/6+1/24+1/60+...+1/6840 < 1/4

d) B= 36/15+36/105+36/315+...+36/19575 < 3

Mn oi!!!!! Giup minh lam 2 bai nay voi!!!!!

Answer 1

Bài 1 :

a) \(\dfrac{42}{43}=1-\dfrac{1}{43}\)

\(\dfrac{58}{59}=1-\dfrac{1}{59}\)

Mà \(\dfrac{1}{43}>\dfrac{1}{59}\Leftrightarrow\dfrac{42}{43}< \dfrac{58}{59}\)

b) \(\dfrac{18}{31}>\dfrac{15}{31}>\dfrac{15}{37}\)

\(\Leftrightarrow\dfrac{18}{31}>\dfrac{15}{37}\)

c) \(\dfrac{53}{57}=1-\dfrac{4}{57}\)

\(\dfrac{531}{517}=1-\dfrac{40}{517}\)

Mà \(\dfrac{4}{57}=\dfrac{40}{570}>\dfrac{40}{517}\)

\(\Leftrightarrow\dfrac{53}{57}< \dfrac{531}{517}\)