Đáp án:
`1/1.2+1/2.3+1/3.4+...+1/999.1000`
`=(2-1)/1.2+(3-2)/2.3+(4-3)/3.4+...+(1000-999)/999.1000`
`=1-1/2+1/2-1/3+1/3-1/4+...+1/999-1/1000`
`=1-1/1000`
`=999/1000`
`1/1.2+2/2.4+3/4.7+4/7.11+5/11.16`
`=(2-1)/1.2+(4-2)/2.4+(7-4)/4.7+(11-7)/7.11+(16-11)/11.16`
`=1-1/2+1/2-1/4+1/4-1/7+1/7-1/11+1/11-1/16`
`=1-1/16`
`=15/16`
`2/2.4+2/4.6+2/6.8+...+2/98.100`
`=(4-2)/2.4+(6-4)/4.6+(8-6)/6.8+...+(100-98)/98.100`
`=1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100`
`=1/2-1/100`
`=49/100`
`2/1.2+2/2.3+2/3.4+...+2/99.100`
`=2(1/1.2+1/2.3+1/3.4+...+1/99.100)`
`=2(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)`
`=2(1-1/100)`
`=2-1/50`
`=99/50`
`(2^4-4^2)*123456789/987654321`
`=(2^4-(2^2)^2)*123456789/987654321`
`=(2^4-2^4)*123456789/987654321`
`=0*123456789/987654321`
`=0`
`1+2+3+4+...+100` (Có `100` số hạng)
`=(1+100)+(2+99)+...` (Có `50` cặp)
`=101+101+...`
`=101*50`
`=5050`
