Tính: `A=1/(1×2×3)+1/(2 ×3 ×4)+…+1/(98 ×99 ×100)`

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1. `1/(1×2×3) + 1/(2×3×4) +…+ 1/(98×99×100)`

   `⇒(1/(1×2) – 1/(2×3)):2 + (1/(2×3) – 1/(3×4)):2 +…+ (1/(98×99) – 1/(99×100)):2`

   `⇒2:(1/(1×2) – 1/(2×3) + 1/(2×3) – 1/(3×4) +…+1/(98×99) – 1/(99×100))`

   `=1/2 – 1/9900`

   Quy đồng `1/2` ta có:

   `⇒(4950/9900 – 1/9900) : 2` 

   `=(4949/9900):2`

   `=4949/19800`

    

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2. `A=1/(1×2×3)+1/(2×3×4)+…+1/(98×99×100)`

   `⇒A=1/2×(2/(1×2×3)+2/(2×3×4)+…+2/(98×99×100))`

   `⇒A=1/2×(1/(1×2)-1/(2×3)+1/(2×3)-1/(3×4)+…+1/(98×99)-1/(99×100))`

   `⇒A=1/2×(1/(1×2)-1/(99×100))`

   `⇒A=1/2×(1/2-1/9900)`

   `⇒A=1/2×(4950/9900-1/9900)`

   `⇒A=1/2×4949/9900`

   `⇒A=4949/19800`

    

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