Toán CMR: A=1/3-2/3^2+3/3^3-4/3^4+…+99/3^99-100/3^100 09/09/2021 By aikhanh CMR: A=1/3-2/3^2+3/3^3-4/3^4+…+99/3^99-100/3^100
Đáp án: Giải thích các bước giải: Ta có:` A=1/3 – 2/3^2+3/3^3 – 4/3^4+ … – 100/3^100``=>3A=1 -2/3 +3/3^2 – 4/3^3+ … – 100/3^99``=>4A=A+3A=1-1/3+1/3^2-1/3^3+…-1/3^99 – 100/3^100``=>12A=3.4A=3-1+1/3-1/3^2+…-1/3^98 – 100/3^99``=>16A=12A+4A=3-1/3^99-100/3^99-100/3^1…``<=> 16A=3-101/3^99-100/3^100``<=> A=3/10-(101/3^99+100/3^100)/16 < 3/10`Suy ra `A<3/10` Trả lời
Đáp án:
Giải thích các bước giải:
Ta có:` A=1/3 – 2/3^2+3/3^3 – 4/3^4+ … – 100/3^100`
`=>3A=1 -2/3 +3/3^2 – 4/3^3+ … – 100/3^99`
`=>4A=A+3A=1-1/3+1/3^2-1/3^3+…-1/3^99 – 100/3^100`
`=>12A=3.4A=3-1+1/3-1/3^2+…-1/3^98 – 100/3^99`
`=>16A=12A+4A=3-1/3^99-100/3^99-100/3^1…`
`<=> 16A=3-101/3^99-100/3^100`
`<=> A=3/10-(101/3^99+100/3^100)/16 < 3/10`
Suy ra `A<3/10`