Question

A=1/10+1/11+....+1/100

chứng tỏ A>1

Answer 1

ta thay tu 1/10 +1/11+............+1/20 >1/20+1/20+........+1/20 =10/20=1/2 

1/21+............+1/30 >1/30+1/30+........+1/30 =10/30=1/3

1/31 +1/32+............+1/40 >1/40+1/40+........+1/40 =10/40=1/4

=>1/10+1/11+-----+1/40>1/2+1/3+1/4=13/12>1

=>a>1 

Answer 2

Chỉ cần 30 số hạng đầu đã lớn hơn 1. 
1/10+1/11+…+1/19 > 1/20+1/20+…+1/20 = 10/20 = 1/2 
1/20+1/21+…+1/29 > 1/30+1/30+…+1/30 = 10/30 = 1/3 
1/30+1/31+…+1/39 > 1/40+1/40+…+1/40 = 10/40 = 1/4 
=> 1/10+1/11+…+1/39 > 1/2+1/3+1/4 = 13/12 > 1

Answer 3

A = 1 / 10 + 1 / 11 + 1 / 12 + ... +  1 / 100  [ có ( 100 - 10 ) : 1 + 1 = 91 số hạng )

=> A > 1 / 10 + 1 / 100  x 90

=> A > 1 / 10 + 90 / 100

=> A > 1 / 10 + 9 / 10 

=> A > 10 / 10

=> A > 1

Vậy A > 1

 

Answer 4

A>1