Question

Cho tổng A = 1/10 + 1/12 + .... + 1/99 + 1/100

Chứng tỏ rằng A >1

Answer 1

1/10>1/40;1/11>1/40;...;1/40=1/40

=>1/10+1/11+...+1/40>1/40+1/40+...+1/=1/40 .31=31/40>1/2                              (1)

1/41>1/100;1/42>1/100;....1/100=1/100

=>1/41+1/42+...+1/100>1/100+1/100+...+1/100=1/100 .60=3/5>1/2                     (2)

Từ (1) và (2) =>A>1/2+1/2=1

Vậy A>1(đpcm)

Answer 2

A = 1/10+ (1/11 + 1/12+ ...+ 1/99 + 1/100)

 A = 1/10 + (1/11 + 1/12 + ..+ 1/99 + 1/100) > 1/10 + (1/100 + 1/100 +... + 1/100)

A = 1/10 + 90/100 = 1

vậy A > 1