Đáp án:
`B=495/202`
`C=8/51`
`A>B`
Giải thích các bước giải:
`B=5/(2.3)+5/(3.4)+...+5/(100.101)`
`=5. (1/(2.3)+1/(3.4)+...+1/(100.101))`
`=5. (1/2-1/3+1/3-1/4+...+1/100-1/101)`
`=5. (1/2-1/101) = 5 . 99/202=495/202`
$\\$
`C=1/15+1/35+...+1/2499`
`2C=2/(3.5)+2/(5.7)+...+2/(49.51)`
`2C=1/3-1/5+1/5-1/7+...+1/49-1/51`
`2C=1/3-1/51=16/51`
`C=8/51`
$\\$
`A=(3^10+1)/(3^9+1)`
`1/3A=(3^9+1/3)/(3^9+1)=(3^9+1-2/3)/(3^9+1)=1-(2/3)/(3^9+1)`
`B=(3^9+1)/(3^8+1)`
`1/3B=(3^8+1/3)/(3^8+1)=(3^8+1-2/3)/(3^8+1)=1-(2/3)/(3^8+1)`
Vì : `3^10+3>3^9+3`
`to (2/3)/(3^10+3)<(2/3)/(3^9+3)`
`to 1-2/(3^10+3)>1-2/(3^9+3)`
`to 1/3A>1/3B`
`to A>B`