Toán So sánh : `C=1/4+frac\{1}{4^2}+frac{1}{4^3}+…+frac{1}{4^100}` với `1/3` 17/07/2021 By Genesis So sánh : `C=1/4+frac\{1}{4^2}+frac{1}{4^3}+…+frac{1}{4^100}` với `1/3`
`C=1/4+1/4^2+1/4^3+…+1/4^100` `⇒4C=1+1/4+1/4^2+…+1/4^99` `⇒4C-C=(1+1/4+1/4^2+…+1/4^99)-(1/4+1/4^2+1/4^3+…+1/4^100)` `⇒3C=1-1/4^100` `⇒C=(1-1/4^100)/3` `\text{Vì}` `1-1/4^100<1` `\text{nên}` `(1-1/4^100)/3<1/3`. `\text{Vậy}` `C<1/3`. Trả lời
Ta có : `4C=1+1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+1/99` `C=1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+frac\{1}{4^99}+frac\{1}{4^100}` `=>4C-C=1-frac\{1}{4^100}` `=>3C=1-frac{1}{4^100}<1` `=>3C<1` `=>C<1/3` Trả lời
`C=1/4+1/4^2+1/4^3+…+1/4^100`
`⇒4C=1+1/4+1/4^2+…+1/4^99`
`⇒4C-C=(1+1/4+1/4^2+…+1/4^99)-(1/4+1/4^2+1/4^3+…+1/4^100)`
`⇒3C=1-1/4^100`
`⇒C=(1-1/4^100)/3`
`\text{Vì}` `1-1/4^100<1` `\text{nên}` `(1-1/4^100)/3<1/3`.
`\text{Vậy}` `C<1/3`.
Ta có :
`4C=1+1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+1/99`
`C=1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+frac\{1}{4^99}+frac\{1}{4^100}`
`=>4C-C=1-frac\{1}{4^100}`
`=>3C=1-frac{1}{4^100}<1`
`=>3C<1`
`=>C<1/3`