A=1+1/3+1/6+1/10+1/15+1/21+1/28+1/36 giúp mình đi mình vật lộn với cái bài này nãy h rùi

Đáp án:

$A=\dfrac{16}9$.

Giải thích các bước giải:

$A=1+\dfrac13+\dfrac16+\dfrac1{10}+\dfrac1{15}+\dfrac1{21}+\dfrac1{28}+\dfrac1{36}\\A=\dfrac 22+\dfrac26+\dfrac2{12}+\dfrac2{20}+\dfrac2{30}+\dfrac2{42}+\dfrac2{56}+\dfrac2{72}\\A=\dfrac2{1\times2}+\dfrac2{2\times3}+\dfrac2{3\times4}+\dfrac2{4\times5}+\dfrac2{5\times6}+\dfrac2{6\times7}+\dfrac2{7\times8}+\dfrac2{8\times9}\\A=2\times\left(\dfrac1{1\times2}+\dfrac1{2\times3}+\dfrac1{3\times4}+\dfrac1{4\times5}+\dfrac1{5\times6}+\dfrac1{6\times7}+\dfrac1{7\times8}+\dfrac1{8\times9}\right)\\A=2\times\left(\dfrac{2-1}{1\times2}+\dfrac{3-2}{2\times3}+\dfrac{4-3}{3\times4}+\dfrac{5-4}{4\times5}+\dfrac{6-5}{5\times6}+\dfrac{7-6}{6\times7}+\dfrac{8-7}{7\times8}+\dfrac{9-8}{8\times9}\right)\\A=2\times\left(1-\dfrac12+\dfrac12-\dfrac13+\dfrac13-\dfrac14+\dfrac14-\dfrac15+\dfrac15-\dfrac16+\dfrac16-\dfrac17+\dfrac17-\dfrac18+\dfrac18-\dfrac19\right)\\A=2\times\left(1-\dfrac19\right)\\A=2\times\dfrac89\\A=\dfrac{16}9$

Đáp án:

$\texttt{d.a.r.i}$

`A = 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36 `

`A =2/2+2/6+2/12+2/20+2/30 + 2/42 + 2/56+2/72`

`A = 2.(1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)`

`A = 2.(1/[1.2] + 1/[2.3] + 1/[3.4] + 1/[4.5] + 1/[5.6] + 1/[6.7] + 1/[7.8] + 1/[8.9])`

`A = 2.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9)`

`A = 2.(1 - 1/9)`

`A = 2. 8/9`

`A = 16/9`