$\color{green}{Tính:}$ $\frac{1}{3}$+$\frac{1}{6}$+$\frac{1}{10}$+$\frac{1}{15}$+…+$\frac{1}{45}$

0 bình luận về “$\color{green}{Tính:}$ $\frac{1}{3}$+$\frac{1}{6}$+$\frac{1}{10}$+$\frac{1}{15}$+…+$\frac{1}{45}$”

1. Hướng dẫn trả lời:

   $\text{$\dfrac{1}{3}$ + $\dfrac{1}{6}$ + $\dfrac{1}{10}$ + $\dfrac{1}{15}$ + … + $\dfrac{1}{45}$.}$

   `= 2/6 + 2/12 + 2/20 + 2/30 + … + 2/90.`

   `= 2.(1/6 + 1/12 + 1/20 + 1/30 + … + 1/90).`

   `= 2.(1/{2.3} + 1/{3.4} + 1/{4.5} + 1/{5.6} + … + 1/{9.10}).`

   `= 2.(1/2-1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/9 – 1/10).`

   `= 2.(1/2 – 1/10).`

   `= 2.(10/20 – 2/20).`

   `= 2. 2/5.`

   `= 4/5.`

   Đáp án:

   `= 4/5.`

   Trả lời

2. Đáp án + Giải thích các bước giải:

   `1/3 + 1/6 + 1/10 + 1/15 + … + 1/45` $\\$ `= 2/6 + 2/12 + 2/20 + 2/30 + … + 2/90` $\\$ `= 2/(2*3) + 2/(3*4) + 2/(4*5) + 2/(5*6) + … + 2/(9*10)` $\\$ `= 2(1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/9 – 1/10)` $\\$ `= 2(1/2 – 1/10) = 2*2/5 = 4/5` 

   Trả lời