5^4+5^8+5^12+...+5^400
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![](https://rs.olm.vn/images/avt/0.png?1311)
) 2 x 6 = 12 3 x 7 = 21
12 : 2 = 6 21 : 3 = 7
12 : 6 = 2 21 : 7 = 3
4 x 8 = 32 5 x 9 = 45
32 : 4 = 8 45 : 5 = 9
32 : 8 = 4 45 : 9 = 5
b) 600 : 3 = 200 800 : 4 = 200 400 : 2 = 200
600 : 2 = 300 800 : 2 = 400 500 : 5 = 100
a) 2x6=12 3x7=21
12:2=6 21:3=7
12:6=2 21:7=3
4x8=32 5x9=45
32:4=8 45:5=9
32:8=4 45:9=5
b) 600:3=200 800:4=200 400:2=200
600:2=300 800:2=400 500:5=100
A Legend Never Dies
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a) (-17) + 5 + 8 + 17
= 17 - 17 + 5 + 8
= 13
b) 30 + 12 + (-20) + (-12)
= 30 - 20 + 12 - 12
= 10
c) (-4) + (-400) + (-6) + 440
= -4 - 6 + 440 - 400
= -10 + 40
= 30
d) (-5) + (-10) + 16 + (-1)
= -5 - 10 + 16 - 1
= 0
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\ln\left(\sqrt{5}+2\right)+\ln\left(\sqrt{5}-2\right)=ln\left(\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\right)=\ln\left(\left(\sqrt{5}\right)^2-2^2\right)=ln\left(5-4\right)=\ln1=\ln e^0=1\)
b) \(\log400-\log4=\log\dfrac{400}{4}=\log100=\log10^{10}=10.\log10=10.1=10\)
c) \(\log_48+\log_412+\log_4\dfrac{32}{2}=\log_4\left(8.12.\dfrac{32}{2}\right)=\log_4\left(1024\right)=\log_44^5=5.\log_44=5.1=5\)
a: \(=ln_2\left[\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\right]=ln1=0\)
b: \(=log\left(\dfrac{400}{4}\right)=log\left(100\right)=10\)
c: \(=log_4\left(8\cdot12\cdot\dfrac{32}{3}\right)=log_4\left(32\cdot32\right)=5\)
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\(\dfrac{4}{5}\) : (\(\dfrac{4}{5}\) .- \(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))
= \(\dfrac{4}{5}\) : (-1) : (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))
= -\(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)
= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)
= - \(\dfrac{20}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{4}{5}\): (\(\dfrac{4}{5}\).-\(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))
=\(\dfrac{4}{5}\) x - 1: (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))
= - \(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)
= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)
= - \(\dfrac{20}{11}\)
\(\dfrac{11}{12}\): (\(\dfrac{7}{9}\) + - \(\dfrac{1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))
= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))
= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)
= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)
= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)
= \(\dfrac{83}{48}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: =1-1+5-5+7-7+8-8=0
2: =14-23+5+14-5+23+17
=28+17=45
3: =12-12+9-9+14-44-3=-33
4: =22-8-8-12+4
=22-16-8
=-2
Bài \(1\)
\(1)\) \(1-5+7-8+4-1+5-7+8\)
\(=(1-1)+(5-5)+(7-7)+(8-8)\)
\(=0+0+0+0\)
\(=0\)
\(2)\) \(14-23+(5+14)-(5-23)+17\)
\(=14-23+5+14-5+23+17\)
\(=(14+14)+(23-23)+(5-5)+17\)
\(=28+17\)
\(=45\)
\(3)\) \(12-44+9-3+14-19-9-12\)
\(=(12-12)+(9-9)+(14-44)+3\)
\(=-30+3\)
\(=-33\)
\(4)\) \(22-(4-8+12)+(-8-12+4)\)
\(=22-4+8-12-8-12+4\)
\(=22+(4+4)+(8-8)+(-12-12)\)
\(=22-24\)
\(=-2\)
625A=5^8+5^12+...+5^404
=>624A=5^404-5^4
=>\(A=\dfrac{5^{404}-5^4}{624}\)