A = 1/31 + 1/32 + 1/33 + ... + 1/89 + 1/90 ..... 5/6
A = 5/6 = 1/2 + 1/3
Ta đặt : B = 1/31 + 1/32 + 1/33 + ... + 1/60 ( 30 phân số )
C = 1/61 + 1/62 + 1/63 + .... + 1/90 ( 30 phân số )
Ta có : B = 1/31 + 1/32 + 1/33 + ... + 1/60 > 1/60 + 1/60 + 1/60 + ... + 1/60 = 30 x 1/60 = 1/2
C = 1/61 + 1/62 + 1/63 + ... + 190 > 1/90 + 1/90 + 1/90 + .... + 1/90 = 30 x 1/90 = 1/3
Vì A = B + C > 1/2 + 1/3 = 5/6 nên 1/31 + 1/32 + 1/33 + .. + 1/89 + 1/90 > 5/6
Đặt \(A=\frac{1}{31}+\frac{1}{32}+....+\frac{1}{60}=\frac{1}{60}.30=\frac{1}{2}\)
Đặt \(B=\frac{1}{61}+\frac{1}{62}+...+\frac{1}{90}=\frac{1}{90}.30=\frac{1}{3}\)
Ta có: \(Q>A+B\Rightarrow Q>\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)
Vậy \(Q=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{90}>\frac{5}{6}\) (đpcm)
Ủng hộ mik nha??