A = 2 + 2 ² + 2 ³ + … + 2 $2^{100}$ Chứng minh chia hết cho 30 Ai xong tước sẽ cs ctlhn nah

Question

A = 2 + 2 ² + 2 ³ + … + 2 $2^{100}$
Chứng minh chia hết cho 30
Ai xong tước sẽ cs ctlhn nah

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Rose 30 phút 2021-10-09T19:58:47+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-09T19:59:50+00:00

    `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`

     

    0
    2021-10-09T19:59:54+00:00

      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 

     

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