tính nhanh:2/7x1/5+2/7x3/10+1/2x2/7 136x75+136x19+5x136+136 1/2+1/4+1/8+..............+1/64+1/128+1/126 1/1x2+1/2x3+1/3x4+1/4x5+.........+1/99x100 2x2/4+2/4x6+2/6x8+........+2/98x100 2/1x3+2/3x5+2/5x7+.......+2/97x99

Đáp án:

 

Giải thích các bước giải:

`a, 2/7 × 1/5 + 2/7 × 3/10 + 1/2 ×2/7`

= `2/7 × ( 1/5 + 3/10 + 1/2 )`

= `2/7 × 1`

= `2/7`

___________

`b, 136 × 75 + 136 × 19 + 5 × 136 + 136`

= `136 × ( 75 + 19 + 5 + 1 )`

= `136 × 100`

= `13600`

___________

`c, 1/2 + 1/4 + 1/8 +.........+ 1/64 +1/128`

= `1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 +...........+ 1/32 - 1/64 + 1/64 - 1/128`

= `1 - 1/128`

= `127/128`

___________

`d, 1/(1×2) + 1/(2×3) +..........+ 1/(99×100)`

= `1 - 1/2 + 1/2 - 1/3 +........+ 1/99 - 1/100`

= `1 - 1/100`

= `99/100`

___________

`e, 2/(2×4) + 2/(4×6) +.............+ 2/(98×100)`

= `1/2 - 1/4 + 1/4 - 1/6 +...............+ 1/98 - 1/100`

= `1/2 - 1/100`

= `49/100`

___________

`i, 2/(1×3) + 2/(3×5) +..............+ 2/(97×99)`

= `1 - 1/3 + 1/3 - 1/5 +.............+ 1/97 - 1/99`

= `1 - 1/99`

= `98/99`