Đáp án:
Giải thích các bước giải:
`1`.
`1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(119xx120`
`=1-1/2+1/2-1/3+1/3-1/4+...+1/119-1/120`
`=1-1/120`
`=119/120`.
`2`. Mình xin sửa lại đề.
`A=3/(2xx4)+3/(4xx6)+3/(6xx8)+...+3/(98xx100`
`=>A/3=1/(2xx4)+1/(4xx6)+1/(6xx8)+...+1/(98xx100`
`=>(2A)/3=2/(2xx4)+2/(4xx6)+2/(6xx8)+...+2/(98xx100)`
`=>(2A)/3=1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100`
`=>(2A)/3=1/2-1/100`
`=>(2A)/3=49/100`
`=>2A=147/100`
`=>A=147/200`
Vậy biểu thức có giá trị là `147/200`.
`3`.
`A=5/(1xx2xx3)+5/(2xx3xx4)+5/(3xx4xx5)+...+5/(98xx99xx100`
`=>A/5=1/(1xx2xx3)+1/(2xx3xx4)+1/(3xx4xx5)+...+1/(98xx99xx100`
`=>(2A)/5=2/(1xx2xx3)+2/(2xx3xx4)+2/(3xx4xx5)+...+2/(98xx99xx100`
`=>(2A)/5=1/(1xx2)-1/(2xx3)+1/(2xx3)-1/(3xx4)+...+1/(98xx99)-1/(99xx100`
`=>(2A)/5=1/2-1/9900`
`=>(2A)/5=4949/9900`
`=>2A=4949/1980`
`=>A=4949/3960`
Vậy biểu thức có giá trị là `4949/3960`.
`4`.
`A=3/2+3/4+3/8+3/16+...+3/1024`
`=>A/3=1/2+1/4+1/8+1/16+...+1/1024`
`=>(2A)/3=2xx(1/2+1/4+1/8+1/16+...+1/1024)`
`=>(2A)/3=1+1/2+1/4+1/8+...+1/512`
`=>(2A)/3-A/3=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)`
`=>A/3=1-1/1024`
`=>A/3=1023/1024`
`=>A=3069/1024`
Vậy giá trị biểu thức là `3069/1024`.
`5`.
`A=1/2+1/10+1/50+1/250+1/1250+1/6250+1/31250`
`=>A/5=1/5xx(1/2+1/10+1/50+1/250+1/1250+1/6250+1/31250)`
`=>A/5=1/10+1/50+1/250+1/1250+1/620+1/31250+1/156250`
`=>(4A)/5=(1/10+1/50+1/250+1/1250+1/620+1/31250+1/156250)-(1/2+1/10+1/50+1/250+1/1250+1/6250+1/31250)`
`=>(4A)/5=1/2-1/156250`
`=>(4A)/5=78124/156250`
`=>4A=78124/31250`
`=>A=19531/31250`
