Question

Chung Minh rang:1+1/2+1/3+1/4+...+1/63 be hon 6

Answer 1

Với mọi k, n Є N+, n ≥ 2 có 1 / (k + 1) + 1 / (k + 2) + ... + 1 / (k + n) < n / (k + 1) 
=> 
1 = 1 
1 / 2 + 1 / 3 < 2 / 2 = 1 
1 / 4 + 1 / 5 + 1 / 6 + 1 / 7 < 4 / 4 = 1 
1 / 8 + ... + 15 < 8 / 8 = 1 
1 / 16 + ... + 1 / 31 < 16 / 16 = 1 
1 / 32 + ... + 1 / 63 < 32 / 32 = 1 
Cộng vế theo vế có 1 + 1 / 2 + ... + 1 / 63 < 6

Answer 2

1+1/2+1/3+1/4+...+1/63=1+(1/2+1/3)+(1/4+1/5+1/6+1/7)+(1/8+1/9+...+1/15)+(1/16+1/17+..,+1/31)+(1/32+1/33+...+1/63)

                                             <1+(1/2+1/2)+(1/4+1/4+1/4+1/4)+(1/8+1/8+...+1/8)+(1/16+1/16+...+1/16)+(1/32+1/32+...+1/32)

                                              <1+1+1+1+1+1=6