A = 2 + 2 ² + 2 ³ + … + 2 $2^{100}$
Chứng minh chia hết cho 30
Ai xong tước sẽ cs ctlhn nah
A = 2 + 2 ² + 2 ³ + … + 2 $2^{100}$ Chứng minh chia hết cho 30 Ai xong tước sẽ cs ctlhn nah
By Rose
By Rose
A = 2 + 2 ² + 2 ³ + … + 2 $2^{100}$
Chứng minh chia hết cho 30
Ai xong tước sẽ cs ctlhn nah
`A=2+2^2+2^3+…+2^100`
`A=(2+2^2+2^3+2^4)+(2^5+2^6+2^7+2^8)+…+(2^97+2^98+2^99+2^100)`
`A=30+2^4(2+2^2+2^3+2^4)+…+2^96(2+2^2+2^3+2^4)`
`A=30+2^4 .30+2^8 .30+…+2^96 .30`
`A=30(1+2^4+2^8+…+2^96)`
`=>A`$\vdots$`30`
A = 2 + 2 ² + 2 ³ + … + $2^{100}$
= ( 2 + 2 ² + 2 ³+ $2^{4}$ ) + … + ( + $2^{97}$ + $2^{98}$ + $2^{99}$ + $2^{100}$
= 2 . ( 2 + 2 ² + 2 ³+ $2^{4}$ ) + … + $2^{97}$ . ( 2 + 2 ² + 2 ³+ $2^{4}$ )
= 2 . 30 + . . . + $2^{97}$ . 30
= 30 + ( 2 + . . . + $2^{97}$ )
Vây A chia hết cho 30