Giải thích các bước giải:
`a) A=1/(1.3)+1/(3.5)+1/(5.7)+..+1/(99.101)`
`=1/2(2/(1.3)+2/(3.5)+...+2/(99.101))`
`=1/2(1-1/3+1/3-1/5+...+1/99-1/101)`
`=1/2(1-1/101)`
`=1/2.(100)/(101)=50/101`
`b) B=1.2+2.3+3.4+..+99.100`
⇒`3B=1.2.3+2.3.3+3.4.3+...+99.100.3`
⇒`3B=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)`
⇒`3B=1.2.3-1.2.3+2.3.4-2.3.4+....+99.100.101`
⇒`3B=99.100.101`
⇒`B=99.100.101:3=333300`