Đáp án:
`B=2000/101`
Giải thích các bước giải:
`B=10+10/(1+2)+10/(1+2+3)+...+10/(1+2+...+100) `
`=>B/10=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+...+100)`
`=>B/10=1+1/3+1/6+...+`$\dfrac{1}{\dfrac{(100+1).100}{2}}$
`=>B/10=1+1/3+1/6+...+`$\dfrac{1}{\dfrac{100.101}{2}}$
`=>B/20=1/2+1/6+1/12+...+1/100.101`
`=>B/20=1/1.2+1/2.3+1/3.4+...+1/100.101`
`=>B/20=1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101`
`=>B/20=1-1/101`
`=>B/20=100/101`
`=>B=100/101*20`
`=>B=2000/101`
Vậy `B=2000/101`.
