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`

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`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`

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`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`

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`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` 

`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`

`---`

`136 × 75 + 136 × 19 + 5 × 136 + 136`

`= 136 × ( 75 + 19 + 5 + 1 )`

`= 136 × 100`

`= 13600`

`---`

`1/2 + 1/4 + 1/8 + ... + 1/64 + 1/128` ( thừa `1/126` )

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

`= 1 - 1/128`

`= 127/128`

`---`

`1/{1 × 2} + 1/{2 × 3} + 1/{3 × 4} + ... + 1/{99 × 100}`

`= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100`

`= 1/1 - 1/100`

`= 99/100`

`---`

`2/{2 × 4} + 2/{4 × 6} + 2/{6 × 8} + ... + 2/{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 × 3} + 2/{3 × 5} + 2/{5 × 7} + ... + 2/{97 × 99}`

`= 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/97 - 1/99`

`= 1/1 - 1/99`

`= 98/99`

`#dtkc`