1/2+1/4+1/8+1/16+1/32+1/64+…….+1/1024+1/2048 25/09/2021 Bởi Maria 1/2+1/4+1/8+1/16+1/32+1/64+…….+1/1024+1/2048
Đặt `A = 1/2 + 1/4 + 1/8 + 1/16 +…+ 1/1024 +1/2048` `A = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^10 + 1/2^11` `2A = 2( 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^10 + 1/2^11)` `2A = 1 + 1/2 + 1/2^2 + 1/2^3+…+ 1/2^10` `2A -A = 1 + 1/2 + 1/2^2 + 1/2^3+…+ 1/2^10- 1/2 – 1/2^2 – 1/2^3-….- 1/2^11)` `A = 1- 1/2^11` Vậy `A = 1- 1/2^11` Bình luận
Đặt: `A=1/2+1/4+1/8+1/16+…+1/1024+1/2048` `=1/2+1/2^2+1/2^3+1/2^4+…+1/2^10+1/2^11` `->2A=1+1/2+1/2^2+1/2^3+…+1/2^9+1/2^10` `->2A-A=(1+1/2+1/2^2+…+1/2^9+1/2^10)-(1/2+1/2^2+1/2^3+…+1/2^10+1/2^11)` `->A=1-1/2^11={2^11-1}/2^11` Bình luận
Đặt `A = 1/2 + 1/4 + 1/8 + 1/16 +…+ 1/1024 +1/2048`
`A = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^10 + 1/2^11`
`2A = 2( 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^10 + 1/2^11)`
`2A = 1 + 1/2 + 1/2^2 + 1/2^3+…+ 1/2^10`
`2A -A = 1 + 1/2 + 1/2^2 + 1/2^3+…+ 1/2^10- 1/2 – 1/2^2 – 1/2^3-….- 1/2^11)`
`A = 1- 1/2^11`
Vậy `A = 1- 1/2^11`
Đặt: `A=1/2+1/4+1/8+1/16+…+1/1024+1/2048`
`=1/2+1/2^2+1/2^3+1/2^4+…+1/2^10+1/2^11`
`->2A=1+1/2+1/2^2+1/2^3+…+1/2^9+1/2^10`
`->2A-A=(1+1/2+1/2^2+…+1/2^9+1/2^10)-(1/2+1/2^2+1/2^3+…+1/2^10+1/2^11)`
`->A=1-1/2^11={2^11-1}/2^11`