Đáp án:
$\text{@sbpro2009}$
Giải thích các bước giải:
`a)`
$x\times\dfrac{3+\dfrac{3}{20}+\dfrac{3}{13}+\dfrac{3}{2013}}{5+\dfrac{5}{20}+\dfrac{5}{13}+\dfrac{5}{2013}}=\dfrac{5}{3}$
`=>`$x\times\dfrac{3\times\left(1+\dfrac{1}{20}+\dfrac{1}{13}+\dfrac{1}{2013}\right)}{5\times\left(1+\dfrac{1}{20}+\dfrac{1}{13}+\dfrac{1}{2013}\right)}=\dfrac{5}{3}$
`=>x xx3/5=5/3`
`=>x=5/3:3/5`
`=>x=25/9`
Vậy `x=25/9`.
`b)``B=1/5+1/13+1/14+1/15+1/61+1/62+1/63`
`=>B=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)`
Ta thấy `1/12>1/13;1/12>1/14;1/12>1/15`
`=>1/13+1/14+1/15<1/12+1/12+1/12`
`=>1/13+1/14+1/15<1/4(1)`
Ta thấy `1/60>1/61;1/60>1/62;1/60>1/63`
`=>1/61+1/62+1/63<1/60+1/60+1/60`
`=>1/61+1/62+1/63<1/20(2)`
Từ `(1)` và `(2)` ta có:
`=>1/13+1/14+1/15+1/61+1/62+1/63<1/4+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/5+1/4+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<9/20+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2`
Vậy `B<1/2`.
