A=1/1+2+1/1+2+3+1/1+2+3+4+…+1/1+2+3+…+150 GIÚP MÌNH VỚI !

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1. A = $\frac{1}{1+2}$ + $\frac{1}{1+2+3}$ + … + $\frac{1}{1+2+..+150}$ 

   A = $\frac{1}{3}$ + $\frac{1}{6}$ + … + $\frac{1}{150.151:2}$ 

   $\frac{1}{2}$ A = $\frac{1}{6}$ + $\frac{1}{12}$ + … + $\frac{1}{150.151}$ 

   $\frac{1}{2}$ A = $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + … + $\frac{1}{150.151}$ 

   $\frac{1}{2}$ A = $\frac{1}{2}$ – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{4}$ + … + $\frac{1}{150}$ – $\frac{1}{151}$ 

   $\frac{1}{2}$ A = $\frac{1}{2}$ – $\frac{1}{151}$ = $\frac{151}{302}$ – $\frac{2}{302}$ = $\frac{149}{302}$ 

   A = $\frac{149}{302}$ . 2 = $\frac{149}{151}$ .

   Vậy A = $\frac{149}{151}$.

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2. Ta có:

   `1+2+3+…+150={(150+1)×150:2}={151×150}/2`

   `A=1/{1+2}+1/{1+2+3}+1/{1+2+3+4}+…+1/{1+2+3+…+150}`

   `A=1/ 3 + 1/ 6 + 1/ {10} +…+1/{{151×150}/2}`

   `A=2× 1/ 6 + 2 × 1/ {12}+ 2 × 1/{20}+…+ 2× 1/{151×150}`

   `A=2 × (1/ 6 +1/ {12} + 1/{20}+…+1/{151×150})`

   `A=2×(1/ 2 – 1/ 3 + 1/ 3 – 1/ 4 + 1/ 4 – 1/ 5 + … + 1/{150}-1/ {151})`

   `A=2× (1/ 2 – 1/ {151})`

   `A=2 × {149}/{302}`

   `A={149}/{151}`

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