2/6 + 2/12 + 2/20 +...+ 2/a+(a + 1)=419/421

$\text{Đáp án + Giải thích các bước giải:}$

`2/6+2/12+2/20+...+2/(a×(a+1))=419/421`

`2×(1/6+1/12+1/20+...+1/(a×(a+1)))=419/421`

`2×(1/(2×3)+1/(3×4)+1/(4×5)+...+1/(a×(a+1)))=419/421`

`2×(1/2-1/3+1/3-1/4+1/4-1/5+...+1/a-1/(a+1))=419/421`

`2×(1/2-1/(a+1))=419/421`

`1/2-1/(a+1)=419/842`

`1/(a+1)=1/421`

`a+1=421`

`a=420`

Vậy `a=420.`

$\color{red}{𝚈ukihiraSoma}$

`2/6 + 2/12 + 2/20 + ...+ 2/(a×(a+1)) = 419/421`

`⇒ 2/(2×3) + 2/(3×4) + 2/(4×5) + ... + 2/(a×(a+1)) = 419/421`

`⇒ 2 × ( 1/(2×3) + 1/(3×4) + 1/(4×5) + ... + 2/(a×(a+1))) = 419/421`

`⇒ 2 × ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + .... + 1/a - 1/(a+1)) = 419/421`

`⇒ 2 × ( 1/2 - 1/(a+1) ) = 419/421`

`⇒ 1/2 - 1/(a+1) = 419/421 ÷ 2`

`⇒ 1/2 - 1/(a+1) = 419/842`

`⇒ 1/(a+1) = 1/2 - 419/842`

`⇒ 1/(a+1) =   1/421`

`⇒ a + 1 = 421`

`⇒ a = 420`

   Vậy `a = 420`