CMR voi moi so nguyen duong n thi B=3^n+2 -2^n+2 +3^n -2^n chia het cho 10
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Những câu hỏi liên quan
Cho A=n3+3n2+2n
a, CMR A chia het cho 3 voi moi so nguyen n
b, Tim gia tri nguyen duong cua n voi n<10 de A chia het cho 15
Cho A=n3+3n2+2n
a, CMR A chia het cho 3 voi moi so nguyen n
b, Tim gia tri nguyen duong cua n voi n<10 de A chia het cho 15
chung minh rang : voi moi so nguyen duong n thi :3n+2 -2n+2 +3n -2n chia het cho 10
\(3^{n+2}-2 ^{n+2}+3^n-2^n=3^{n+2}+3^n-\left(2^{n+2}+2^n\right)=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)
\(=3^n.10-2^n.5=3^n.10-2^{n-1}.10=\left(2^n-2^{n-1}\right).10\) chia hết cho 10
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chung minh rang voi moi N nguyen duong thi 3^n+2 - 2^n+2 + 3^n - 2^n chia het cho 10
3^n+2-2^n+2+3^n-2^n
=3^n+2+3^n-(2^n+2+2^n)
=3^n(3^2+1)-2^n(2^2+1)
=3^n.10-2^n.5=3^n.10-2^n-1.10=10(3^n-2^n-1) chia hết cho 10(đpcm)
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CMR:Voi moi so nguyen duong N thi:
\(^{3^{2+n}-2^{2+n}+3^n-2^n}\)chia het cho 10
Ta có:
\(3^{2+n}-2^{2+n}+3^n-2^n\)
\(=3^2.3^n-2^2.2^n+3^n-2^n\)
\(=9.3^n-4.2^n+3^n-2^n\)
\(=3^n\left(9+1\right)-2^n\left(4+1\right)\)
\(=10.3^n-5.2^n\)
\(=10.3^n-5.2.2^{n-1}\)
\(=10.3^n-10.2^{n-1}⋮10\left(đpcm\right)\) (n nguyên dương)
CMR : \(3^{n+2}-2^{n+4}+3^n+2^2\)chia het cho 30 voi moi n nguyen duong
Ta có : 3^n+2 - 2^n+4 + 3^n + 2^n
= (3^n+2 + 3^n) - (2^n+4-2^n)
= 3^n-1.(3^3+3) - 2^n-1.(2^5-2) ( vì n nguyên dương nên n-1 >= 0 )
= 3^n-1.30 - 2^n-1.30
= 30.(3^n-1+2^n-1) chia hết cho 30
=> ĐPCM
Tk mk nha
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CMR VOI moi so n nguyen duong deu co A=5^nx(5^n +1)-6^nx(3^n +2) chia het cho 91,giup minh nha
cmr voi moi son nguyen duong deu co A=5^n(5^n+1)-6^n(3^n+2)chia het cho 91
Chung minh rang: Voi moi so nguyen duong n thi: 3n+2 - 2n+2 + 3n - 2n chia het cho 10
GIUP MIK VS MOI NGUOI OI!
\(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)
\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)
\(=3^n\left(9+1\right)-2^{n-1}.2.\left(4+1\right)\)
\(=3^n.10-2^{n-1}.10\)
\(=10\left(3^n-2^{n-1}\right)⋮10\) (đpcm)
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Đặt S = 3^(n+2)-2^(n+2)+3^n-2^n = 3^(n+2) + 3^n - [2^(n+2) + 2^n]
Ta có 3^(n+2) + 3^n = 9.3^n + 3^n = 10.3^n (chia hết cho 10)
Và 2^(n+2) + 2^n = 4.2^n + 2^n = 5.2^n (chia hết cho 10, vì chia hết cho 2 và 5)
Suy ra S chia hết cho 10.
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=(\(3^{n+2}+3^n\))-(\(2^{n+2}+2^n\))
=\(3^n.\left(3^2+1\right)-2^n.\left(2^2+1\right)\)
=\(3^n.10-2^{n-1}.10\)
=\(10.\left(3^n-2^{n-1}\right)\)chia hết cho 10
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