Question

\(\dfrac{1}{5}+\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^{100}}+\dfrac{1}{5^{101}}\)

GIÚP MIK TỪNG BƯỚC 1 NHÉ

Answer 1

\(A=\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{101}}\)

\(5A=1+\dfrac{1}{5}+...+\dfrac{1}{5^{100}}\)

\(5A-A=1+\dfrac{1}{5}+...+\dfrac{1}{5^{100}}-\dfrac{1}{5}-\dfrac{1}{5^2}-...-\dfrac{1}{5^{101}}=1-\dfrac{1}{5^{101}}\Rightarrow A=\dfrac{1-\dfrac{1}{5^{101}}}{4}\)

Answer 2

Đặt `B=1/5+1/5^{2}+1/5^{3}+...+1/5^{101}`

`<=>5B=1+1/5+1/5^{2}+...+1/5^{100}`

`<=>5B-B=(1+1/5+1/5^{2}+...+1/5^{100})-(1/5+1/5^{2}+...+1/5^{101})`

`<=>5B-B=1+1/5+1/5^{2}+...+1/5^{100}-1/5-1/5^{2}-...-1/5^{101}`

`<=>4B=1-1/5^{101}`

`<=>B=(1-1/5^{101})/4`

`@Shả`