cho S = 1/2 +1/3 +1/4+....+1/48+1/49+1/50 và P = 1/49+2/48+347+....+48/2+49/1 hãy tính S/P

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`P = 1/49 + 2/48 + ... + 48/2+ 49/1`

`-> P = 1/49 + 2/48 + ... + 48/2 + 49`

`-> P = 1/49 + 1/48 + ... + 48/2 + \underbrace{1+1+...+1}_{\text{49 số 1}}`

`-> P = (1/49 + 1)+(1/48+1)+...+(48/2+1)+1`

`-> P =(1/49 + 49/49)+(1/48 + 48/48)+...+(48/2 + 2/2)+50/50`

`-> P = 50/49 + 50/48 + ... + 50/2 + 50/50`

`-> P =50 (1/2 + 1/3+...+1/49 + 1/50)`

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`S/P`

`= (1/2+1/3+...+1/49+1/50)/(50 (1/2 + 1/3+...+1/49+1/50) )`

`= (\cancel (1/2 +1/3+...+1/49+1/50) )/(50 (\cancel (1/2+1/3+...+1/49+1/50) )`

`= 1/50`

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Vậy `S/P =1/50`