T = 1/1×2 + 1/2×3 + 1/3×4 + … + 1/99×100

0 bình luận về “T = 1/1×2 + 1/2×3 + 1/3×4 + … + 1/99×100”

1. T = `\frac{1}{1×2}` +$\frac{1}{2×3}$ +$\frac{1}{3×4}$ + …. + $\frac{1}{99×100}$ 

   ta có :

   $\frac{1}{1 x 2}$ = `1/1` – `1/2`

   $\frac{1}{2 x 3}$ = `1/2` – `1/3`

   $\frac{1}{3 x 4}$   = `1/3` – `1/4`

   ………..

   $\frac{1}{99 x 100}$ = `1/99` – `1/100`

   ⇒  T = `\frac{1}{1×2}` +$\frac{1}{2×3}$ +$\frac{1}{3×4}$ + …. + $\frac{1}{99×100}$ 

     = `1/1` – `1/2` + `1/2` – `1/3` + `1/3` – `1/4` +….. + `1/99` – `1/100`

   = `1/1` – `1/100`

   = `100/100` – `1/100`

   = `99/100`

   Vậy T = `99/100`

   Bình luận

2. `T = 1/(1xx2) + 1/(2xx3) + 1/(3xx4) + … + 1/(99xx100)`

   `= 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/99 – 1/100`

   `= 1 – 1/100`

   `= 100/100 – 1/100`

   `= 99/100`

   Bình luận