Đáp án `+` Giải thích các bước giải:

 `a,` Đặt `A=1+ 1/2+1/3+...+1/(2^2026)`

`A=1+(1/2+ 1/3)+ (1/4+...+1/7)+(1/8+...+1/15)+...+(1/(2^2015)+...+1/(2^2026- 1))+ 1/(2^2026)`

`A<1+ 5/6+ 1/4. 4+ 1/8. 8+...+ 1/(2^2015). 2^2015+ 1/(2^2026)`

`A<1+1+1+1+...+1+ 1/(2^2026)+ 5/6<2025+ 5/6+ 1/6=2026`

`=>A<2026` `(đpcm)`

`b,` Đặt `B=1+ 1/2+ 1/3+...+ 1/(2^1999)`

`B=(1+ 1/2)+(1/3+ 1/4)+(1/5+...+1/8)+...+(1/(2^1998+1)+...+1/(2^1999))`

`B>1+1/2+ 1/4.2+ 1/8.4+...+ 1/(2^1999). 2^1988`

`B>1+ 1/2+ 1/2. 1988`

`B>1000+ 1/2>1000`

`=>B>1000` `(đpcm)`