M=1+1/3-1/3^2+……………+1/3^19-1/3^20 Giúp mình với mn ơi 01/11/2021 Bởi Faith M=1+1/3-1/3^2+……………+1/3^19-1/3^20 Giúp mình với mn ơi
`M=1+1/3-1/3^2+…+1/3^19-1/3^20` `⇒3M=3+1-1/3+…+1/3^18-1/3^19` `⇒3M+M=3+1-1/3+…+1/3^18-1/3^19+1+1/3-1/3^2+…+1/3^19-1/3^20` `⇒4M=(3+1+1)-(1/3+…+1/3^18-1/3^19+1/3-1/3^2+…+1/3^19)-1/3^20` `⇒4M=5-1/3^20` `⇒M=5/4-1/3^20.4` `⇒M=5.3^20-1/3^20.4` Bình luận
$M=1+\frac{1}{3}-$ $\frac{1}{3^2}+…-$ $\frac{1}{3^{20}}$ => $3M=3+1-\frac{1}{3}+…-$ $\frac{1}{3^{19}}$ => $M+3M=(1+3+1)+($$\frac{1}{3}-$ $\frac{1}{3})+…-$ $\frac{1}{3^{20}}$ => $4M=5-$$\frac{1}{3^{20}}$ => $M=\frac{5}{4}-$ $\frac{1}{3^{20}.4}$ => M=$\frac{5.3^{20}-1}{3^{20}.4}$ Bình luận
`M=1+1/3-1/3^2+…+1/3^19-1/3^20`
`⇒3M=3+1-1/3+…+1/3^18-1/3^19`
`⇒3M+M=3+1-1/3+…+1/3^18-1/3^19+1+1/3-1/3^2+…+1/3^19-1/3^20`
`⇒4M=(3+1+1)-(1/3+…+1/3^18-1/3^19+1/3-1/3^2+…+1/3^19)-1/3^20`
`⇒4M=5-1/3^20`
`⇒M=5/4-1/3^20.4`
`⇒M=5.3^20-1/3^20.4`
$M=1+\frac{1}{3}-$ $\frac{1}{3^2}+…-$ $\frac{1}{3^{20}}$
=> $3M=3+1-\frac{1}{3}+…-$ $\frac{1}{3^{19}}$
=> $M+3M=(1+3+1)+($$\frac{1}{3}-$ $\frac{1}{3})+…-$ $\frac{1}{3^{20}}$
=> $4M=5-$$\frac{1}{3^{20}}$
=> $M=\frac{5}{4}-$ $\frac{1}{3^{20}.4}$
=> M=$\frac{5.3^{20}-1}{3^{20}.4}$