Toán $S=$ $\frac{1}{4}$ + $\frac{1}{4^{2}}$ + $\frac{1}{4^{3}}$ + … + $\frac{1}{4^{50}}$ 21/11/2021 By Maya $S=$ $\frac{1}{4}$ + $\frac{1}{4^{2}}$ + $\frac{1}{4^{3}}$ + … + $\frac{1}{4^{50}}$
`S=1/4+1/4^2+1/4^3+…+1/4^50` `=> 1/4 S = 1/4(1/4+1/4^2+1/4^3+…+1/4^50)` `⇒ 1/4 S = 1/4^2 + 1/4^3 + 1/4^4 +…+ 1/4^51` `⇒ S – 1/4 S = (1/4+1/4^2+1/4^3+…+1/4^50)-(1/4^2 + 1/4^3 + 1/4^4 +…+ 1/4^51)` `⇒ 3/4 S = 1/4 – 1/4^51` `⇒ S = (1/4 – 1/4^51) : 3/4` `⇒ S = (1/4 – 1/4^51) . 4/3` `⇒ S = 1/3 – 1/(4^50 . 3)` Trả lời
$S=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+…+\frac{1}{4^{50}}$ $⇒4S=\frac{4}{4}+\frac{4}{4^2}+\frac{4}{4^3}+…+\frac{4}{4^{50}}$ $⇒4S=1+\frac{1}{4}+\frac{1}{4^2}+…+\frac{1}{4^{49}}$ $⇒4S-S=(1+\frac{1}{4}+\frac{1}{4^2}+…+\frac{1}{4^{49}})-(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+…+\frac{1}{4^{50}})$ $⇒3S=1-\frac{1}{4^{50}}$ $⇒S=\frac{1}{3}-\frac{1}{3.4^{50}}$. Trả lời
`S=1/4+1/4^2+1/4^3+…+1/4^50`
`=> 1/4 S = 1/4(1/4+1/4^2+1/4^3+…+1/4^50)`
`⇒ 1/4 S = 1/4^2 + 1/4^3 + 1/4^4 +…+ 1/4^51`
`⇒ S – 1/4 S = (1/4+1/4^2+1/4^3+…+1/4^50)-(1/4^2 + 1/4^3 + 1/4^4 +…+ 1/4^51)`
`⇒ 3/4 S = 1/4 – 1/4^51`
`⇒ S = (1/4 – 1/4^51) : 3/4`
`⇒ S = (1/4 – 1/4^51) . 4/3`
`⇒ S = 1/3 – 1/(4^50 . 3)`
$S=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+…+\frac{1}{4^{50}}$
$⇒4S=\frac{4}{4}+\frac{4}{4^2}+\frac{4}{4^3}+…+\frac{4}{4^{50}}$
$⇒4S=1+\frac{1}{4}+\frac{1}{4^2}+…+\frac{1}{4^{49}}$
$⇒4S-S=(1+\frac{1}{4}+\frac{1}{4^2}+…+\frac{1}{4^{49}})-(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+…+\frac{1}{4^{50}})$
$⇒3S=1-\frac{1}{4^{50}}$
$⇒S=\frac{1}{3}-\frac{1}{3.4^{50}}$.