Tính,6 câu 60 điểm 1/1.2+1/2.3+1/3.4+…+1/999.1000 1/1.2+2/2.4+3/4.7+4/7.11+5/11.16 2/2.4+2/4.6+2/6.8+…+2/98.100 2/1.2+1/2.3+2/3.4+….+2/99.100 (2

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`