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ta có : \(A=1+3+3^2+...+3^{99}\)
\(\Rightarrow3A=3\left(1+3+3^2+...+3^{99}\right)\)
\(\Leftrightarrow3A=3+3^2+3^3+...+3^{100}\)
\(\Rightarrow3A-A=2A=\left(3+3^2+3^3+...+3^{100}\right)-\left(1+3+3^2+...+3^{99}\right)\)
\(\Leftrightarrow2A=3^{100}-1\)
\(\Rightarrow2A+1=3^{100}-1+1=3^{100}=\left(3^{25}\right)^4\)
vậy \(2A+1=\left(3^{25}\right)^4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=1+3+3^2+...+3^{41}\)
\(3A=3+3^2+3^3+...+3^{42}\)
\(3A-A=3+3^2+...+3^{42}-1-3-...-3^{41}\)
\(2A=3^{42}-1\)
\(A=\dfrac{3^{42}-1}{2}\)
Ta có: \(2A+1\)
\(=2\cdot\dfrac{3^{42}-1}{2}+1\)
\(=3^{42}-1+1\)
\(=3^{42}\)
\(=\left(3^2\right)^{21}\)
\(=9^{21}\)
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`2^5 . 8^4 = 2^5 . (2^3)^4 = 2^5 . 2^12 = 2^17`
`25^6 . 125^3 = (5^2)^6 . (5^3)^3 = 5^12 . 5^9 = 5^21`
`625^5 : 25^7 = (5^4)^7 : (5^2)^7 = 5^28 : 5^14 = 5^14`
`12^3 . 3^3 = (12 . 3)^3 = 36^3`
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1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
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Ta coi \(B=2^1+2^2+2^3+...+2^{100}\)
\(\Rightarrow A=B+2\)
Ta có:
\(B=2^1+2^2+2^3+...+2^{100}\)
\(\Rightarrow2B=\left(2^1+2^2+2^3+...+2^{100}\right).2\)
\(=2^2+2^3+2^4+...+2^{101}\)
\(\Rightarrow B=2B-B=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)\)
\(=2^{101}-2\)
\(\Rightarrow A=2^{101}-2+2=2^{101}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2S=2^3+2^3+2^4+...+2^{21}\\ S=2^{21}+2^3-2^2-2^2=2^{21}+8-4-4=2^{21}\)
A=1+3+3^2+...+3^99
3A=3+3^2+3^3+...+3^100
3A-A=3^100-1
2A=3^100-1
A=(3^100-1):2
mik chỉ làm được đến đó thôi
A=1+3+3^2+...+3^99
3A=3+3^2+3^3+...+3^100
3A-A=2A=3^100-1
\(\Rightarrow\)2A+1=3^100
Khong viet dc vi 3^100 le ma 4^n chan