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Toán Lớp 7: `A=3^99-3^98+3^97-3^96+-+3^3-3^2+3-1.CMR: A vdots4`

Home/ Toán Lớp 7: `A=3^99-3^98+3^97-3^96+-+3^3-3^2+3-1.CMR: A vdots4`

Toán Lớp 7: `A=3^99-3^98+3^97-3^96+-+3^3-3^2+3-1.CMR: A vdots4`

Huyền Linh Tháng Tám 11, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: A=3^99-3^98+3^97-3^96+….+3^3-3^2+3-1.CMR: A vdots4

Comments ( 1 )

maingocquynhnhu2k1
11 Tháng Tám, 2022 at 8:33 sáng

Reply

A=3^99 -3^98+ 3^97 -3^96+…+3^3 -3^2+3-1

=>3A=(3^100+ 3^98+…+3^4+3^2)-(3^99+ 3^97+…+3^3+3)

=>3A-A=3.(3^98+ 3^96+…+3^2)-(3^98+ 3^96+…+3^2)

3A=(3-1).(3^98+ 3^96+…+3^2)

3A=2.(3^98+ 3^96+…+3^2)

=>3A=2(3^100+ 3^98+…+3^2)

=>A=(2.(3^99+ 3^97+…+3).3)/3

=>A=2.(3^99 + 3^97+…+3)

=>A=2.[(3^99+3^97)+…+(3^3+3)]

=>A=2.[3^97.(3^2+1)+…+3(3^2+1)]

=>A=2.(3^97.10+…+3.10)

=>A=2.10.(3^97+…+3)

=>A=20.(3^97+ 3^95+…+3)

Vì 20 vdots 4=>20.(3^97 + 3^95+…+3) vdots 4=>A vdots 4

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