Đáp án:
`5^2|2x-1|=1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+....+100)`
`-> 25|2x-1|=A`
Ta có: `A=1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+....+100)`
`=1+1/2. (2.3)/2 + 1/3 . (3.4)/2+....+1/100. (100.101)/2`
`=2/2+3/2+...+101/2`
`=(2+3+...+101)/2`
`=5150/2=2575`
`-> 25|2x-1|=2575`
`-> |2x-1|=2575:25=103`
`->` \(\left[ \begin{array}{l}2x-1=103\\2x-1=-103\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=52\\x=-51\end{array} \right.\)