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A=30.32.34....32012.32014=30+2+4+...+2012+2014=32(1+2+3+...+1007)
Ta có: 1+2+3+...+1007=1007(1007+1):2=507528
=> A=32.507528=31015056
\(A=1+5+5^2+..+5^{49}+5^{50}\)
\(5A=5+5^2+5^3+...+5^{50}+5^{51}\)
\(5A-A=\left(5+5^2+5^3+...+5^{51}\right)-\left(1+5+5^2+...+5^{50}\right)\)
\(4A=\left(5-5\right)+\left(5^2-5^2\right)+...+\left(5^{50}+5^{50}\right)+5^{51}-1\)
\(4A=0+0+...+0+5^{51}-1\)
\(4A=5^{51}-1\)
\(A=\frac{5^{51}-1}{4}\)
\(A=3^0+3^1+3^2+3^3+3^4+....+3^{2014}\)
\(A.3=\left(3^0+3^1+3^2+3^3+3^4+....+3^{2014}\right).3\)
\(A.3=3^1+3^2+3^3+3^4+....+3^{2015}\)
\(A.3=\left(3^0+3^1+3^2+3^3+3^4+.....+3^{2014}\right)+3^{2015}-3\)
\(A.3=A+3^{2015}-3\)
\(A.2=3^{2015}-3\)( CUNG BOT DI A)
\(A=\frac{3^{2015}-3}{2}\)
nhớ **** mình nha
\(A=3^0+3^1+3^2+......+3^{2018}\)
\(3A=3.\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(3A=3^1+3^2+3^3+........+3^{2019}\)
\(3A-A=\left(3^1+3^2+3^3+......+3^{2019}\right)-\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(2A=3^{2019}-3^0\)
\(A=\left(3^{2019}-3^0\right):2\)
\(B=6^{10}+6^{11}+6^{12}+....+6^{2012}\)
\(6B=6.\left(6^{10}+6^{11}+6^{12}+.....+6^{2012}\right)\)
\(6B=6^{11}+6^{12}+6^{13}+.......+6^{2013}\)
\(6B-B=\left(6^{11}+6^{12}+6^{13}+......+6^{2013}\right)-\left(6^{10}+6^{11}+6^{12}+.......+6^{2012}\right)\)
\(5B=6^{2013}-6^{10}\)
\(B=\left(6^{2013}-6^{10}\right):5\)
a, (0,25)3.32
= 0,5
b, \(\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)\(=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}\)
\(=\dfrac{2^{11}.3^{12}}{2^8.3^{12}}=2^3\)
c, \(\dfrac{81^{11}.3^{17}}{27^{10}.9^{15}}=\dfrac{\left(3^4\right)^{11}.3^{17}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\dfrac{3^{44}.3^{17}}{3^{30}.3^{30}}\)\(=\dfrac{3^{61}}{3^{60}}=3\)
@Lớp 6B Đoàn Kết
Ta có:
\(8^3:8^4=\left(2^3\right)^3:\left(2^3\right)^4\)
\(=2^9:2^{12}=2^{9-12}=2^{-3}\)
Hình như có gì sai sai đó
\(A=\frac{11.9^{11}.3^7-27^{10}}{\left(2.3^{14}\right)^2}\)
\(A=\frac{11.3^{22}.3^7-3^{30}}{2^2.3^{28}}\)
\(A=\frac{11.3^{29}-3^{30}}{4.3^{28}}\)
\(A=\frac{3^{29}.\left(11-3\right)}{4.3^{28}}\)
\(A=\frac{3.8}{4}\)
\(A=\frac{24}{4}\)
\(A=6\)
vậy \(A=6\)
học tôt Ngô Thị Diệu Linh