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\(A=1+5+5^2+5^3+...+5^{2015}\)
\(5A=5.\left(1+5+5^2+5^3+...+5^{2015}\right)\)
\(=5+5^2+5^3+5^4+...+5^{2016}\)
\(5A-A=\left(5+5^2+5^3+5^4+...+5^{2016}\right)-\left(1+5+5^2+5^3+...+5^{2015}\right)\)
\(4A=5^{2016}-1\)
\(A=\frac{5^{2016}-1}{4}\)
\(=\left[\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}\right)+\frac{1}{5}\left(\frac{1}{9}-\frac{1}{14}\right)+\frac{1}{5}\left(\frac{1}{14}-\frac{1}{19}\right)+...+\frac{1}{5}\left(\frac{1}{44}-\frac{1}{49}\right)\right]\cdot\frac{1-\left(3+5+...+49\right)}{89}\)
\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-...+\frac{1}{44}-\frac{1}{49}\right)\cdot\frac{1-\left(52+52+...+52\right)\left\{12\text{ số 52}\right\}}{89}\)
\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)\cdot\frac{1-624}{89}\)
\(=\frac{9}{196}\cdot-7=\frac{9}{28}\)
\(Q=165+247+528+125+315\)
\(=\left(247+528+125\right)+\left(165+315\right)\)
\(=900+480\)
\(=1280\)
\(R=1000+200+30+4+5000+600+70+8+80\)
\(=\left(1000+5000\right)+\left(200+600\right)+\left(30+70+80\right)+\left(4+8+8\right)\)
\(=6000+800+180+20\)
\(=6000+\left(800+100\right)+\left(80+20\right)\)
\(=6000+900+100\)
\(=7000\)
\(\frac{2^5.15^4}{5^4.6^3}=\frac{2^5.\left(3.5\right)^4}{5^4.\left(2.3^3\right)}=\frac{2^5.3^4.5^4}{5^4.2^3.3^3}=\frac{2^5.3^4.5^4}{2^3.3^3.5^4}=2^2.3=4.3=12\)
k cho mik nha
Bài làm
\(5\sqrt{16}-4\sqrt{9}+\sqrt{25}-0,3\sqrt{400}\)
= \(5.4-4.3+5-0,3.20\)
= \(20-12+5-6\)
= \(8+\left(-1\right)\)
= \(7\)
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