tính tổng s=1/5+1/25+1/125+...+1/5^n

Đáp án:

 `S = 1/5 + 1/25 + 1/125 + .......... + 1/(5^n)`

`5S = 1 + 1/5 + 1/25 + .......... + 1/(5^(n + 1))`

`5S - S = (1 + 1/5 + 1/25 + ......... + 1/(5^(n+1)) ) - (1/5 + 1/25 + 1/125 + 1/(5^n))`

 `4S = 1/(5^(n+1)) - 1/5`

`S   = (1/(5^(n+1)) - 1/5)/4`

Đáp án:

`text(S)=1/4-1/(4.5^(n))`

Giải thích các bước giải:

`text(S)=1/5+1/25+1/125+...+1/5^n`

`=>text(S)=1/5+1/5^2+1/5^3+...+1/5^n`

`=>5text(S)=5.(1/5+1/5^2+1/5^3+...+1/5^n)`

`=>5text(S)=1+1/5+1/5^2+...+1/(5^(n-1))`

`=>5text(S)-\text(S)=(1+1/5+1/5^2+...+1/(5^(n-1)))-(1/5+1/25+1/125+...+1/5^n)`

`=>4text(S)=1-1/(5^n)`

`=>`$\rm S=\dfrac{1-\dfrac{1}{5^{n}}}{4}$

`=>text(S)=1/4-1/(4.5^(n))`

Vậy `text(S)=1/4-1/(4.5^(n))`.