(1+2+2^2+2^3+…+2^99)-2^100 Thực hiện phép tính 01/12/2021 Bởi Kinsley (1+2+2^2+2^3+…+2^99)-2^100 Thực hiện phép tính
Gửi bạn ạ. Cho xin 5*và ctlhn có đc ko ạ. ĐặtA=1+2+22+…+299;B=(1+2+22+23+…+299)−2100A=1+2+22+…+299;B=(1+2+22+23+…+299)-2100 2A=2+22+23+…+21002A=2+22+23+…+2100 2A−A=(2+22+23+…+2100)−(1+2+22+…+299)2A-A=(2+22+23+…+2100)-(1+2+22+…+299) A=2100−1A=2100-1 ⇒B=A−1⇒B=A-1 =2100−1−2100=2100-1-2100 =−1=-1 Bình luận
Đáp án: Đặt `A=1+2+2^2+…+2^99; B=(1+2+2^2+2^3+…+2^99)-2^100` `2A=2+2^2+2^3+…+2^100` `2A-A=(2+2^2+2^3+…+2^100)-(1+2+2^2+…+2^99)` `A=2^100-1` `=> B=A-1` `=2^100-1-2^100` `=-1` Bình luận
Gửi bạn ạ. Cho xin 5*và ctlhn có đc ko ạ.
ĐặtA=1+2+22+…+299;B=(1+2+22+23+…+299)−2100A=1+2+22+…+299;B=(1+2+22+23+…+299)-2100
2A=2+22+23+…+21002A=2+22+23+…+2100
2A−A=(2+22+23+…+2100)−(1+2+22+…+299)2A-A=(2+22+23+…+2100)-(1+2+22+…+299)
A=2100−1A=2100-1
⇒B=A−1⇒B=A-1
=2100−1−2100=2100-1-2100
=−1=-1
Đáp án:
Đặt `A=1+2+2^2+…+2^99; B=(1+2+2^2+2^3+…+2^99)-2^100`
`2A=2+2^2+2^3+…+2^100`
`2A-A=(2+2^2+2^3+…+2^100)-(1+2+2^2+…+2^99)`
`A=2^100-1`
`=> B=A-1`
`=2^100-1-2^100`
`=-1`