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))`.
