Đáp án:
Giải thích các bước giải:
a) `1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(99xx100)`
`=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100`
`=1-1/100`
`=99/100`
b) `A=1+1/3+1/9+1/27+...+1/243+1/729`
`=>3A=3xx(1+1/3+1/9+1/27+...+1/243+1/729)`
`=>3A=3+1+1/3+1/9+...+1/81+1/243`
`=>3A-A=(3+1+1/3+1/9+...+1/81+1/243)-(1+1/3+1/9+1/27+...+1/243+1/729)`
`=>2A=3-1/729`
`=>2A=2186/729`
`=>`$A=\dfrac{2186}{729}:2$
`=>A=1093/729`
Vậy biểu thức có giá trị là `1093/729`.
c) `(1-1/2)xx(1-1/3)xx(1-1/4)xx...xx(1-1/2020)xx(1-1/2021)`
`=1/2xx2/3xx3/4xx...xx2019/2020xx2020/2021`
`=(1xx2xx3xx...xx20219xx2020)/(2xx3xx4xx...xx2020xx2021)`
`=1/2021`
