Ta có 1+5/28=33/28
Đặt A=1/11+1/12+1/13+...+1/69+1/70
A=(1/11+1/12++1/13+...+1/20)+(1/21+1/22+1/23+...+1/30)+(1/31+1/32+1/33+...1/60)+...+1/70
Ta thấy :
1/11+1/12+1/13+...+1/20>1/20+1/20+1/20+...+1/20(có 10 số hạng 1/20)=1/20*10=1/2
1/21+1/22+1/23+...+1/30>1/30+1/30+1/30+...+1/30(10 số hạng 1/30)=1/30*10=1/3
1/30+1/31+1/32+...+1/60>1/60+1/60+...+1/60(30 số hạng 1/60)=1/60*30=1/2
1/61+1/62+1/63+...+1/70>1/70+1/70+1/70+...+1/70(10 số hạng 1/70)=1/70*10=1/7
=>1/11+1/12+1/13+...+1/69+1/70>1/2+1/3+1/2+1/7
=>A>31/21
Mà 31/21>33/28
=>A>33/28
=>A>1+5/28(DPCM)
Vậy A>1+5/28
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