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16 tháng 11 2020
B=1+1/2*(1+2)*2/2+1/3*(1+3)*3/2+....+1/30*(1+30)*30/2
=1+1+2/2+1+3/2+...+1+30/2
=2+3+4+...+31/2
=(31+2)*30/2 phần 2
=) B=247,5
27 tháng 12 2017
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28 tháng 12 2017
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16 tháng 10 2021
\(1,\\ a,\Leftrightarrow x-\dfrac{1}{3}=0\Leftrightarrow x=\dfrac{1}{3}\\ b,\Leftrightarrow\left[{}\begin{matrix}x-4=4\\x-4=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=0\end{matrix}\right.\\ c,\Leftrightarrow2x+1=-2\Leftrightarrow x=-\dfrac{3}{2}\\ 2,\\ a,=1\\ b,=\left(\dfrac{13}{4}\right)^2=\dfrac{169}{16}\\ c,=\left(-\dfrac{7}{4}\right)^2=\dfrac{49}{16}\\ d,=\left(\dfrac{3}{7}\right)^{20}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^8=...\\ e,=\left(3\cdot5\cdot\dfrac{2}{3}\right)^2=10^2=100\)
KN
28 tháng 6 2019
c) Đặt \(A=2^0+2^1+2^2+...+2^{50}\)
\(\Leftrightarrow2A=2^1+2^2+2^3...+2^{51}\)
\(\Leftrightarrow2A-A=2^1+2^2+2^3...+2^{51}\)\(-2^0-2^1-2^2-...-2^{50}\)
\(\Leftrightarrow A=2^{51}-2^0=2^{51}-1< 2^{51}\)
Vậy \(2^0+2^1+2^2+...+2^{50}< 2^{51}\)
KN
28 tháng 6 2019
a)Ta có: \(\hept{\begin{cases}2^{30}=\left(2^3\right)^{10}=8^{10}\\3^{30}=\left(3^3\right)^{10}=27^{10}\\4^{30}=\left(2^2\right)^{30}=2^{60}\end{cases}}\)và \(\hept{\begin{cases}3^{20}=\left(3^2\right)^{10}=9^{10}\\6^{20}=\left(6^2\right)^{10}=36^{10}\\8^{20}=\left(2^3\right)^{20}=2^{60}\end{cases}}\)
Mà \(8^{10}< 9^{10}\); \(27^{10}< 36^{10}\);\(2^{60}=2^{60}\)nên
\(8^{10}+27^{10}+2^{60}< 9^{10}+36^{10}+2^{60}\)
hay \(2^{30}+3^{30}+4^{30}< 3^{20}+6^{20}+8^{20}\)
8 tháng 8 2017
\(VT=1+2+2^3+...+2^{100}\)
\(2VT=2\left(1+2+2^3+...+2^{100}\right)\)
\(2VT=2+2^2+2^3+...+2^{101}\)
\(2VT-VT=\left(2+2^2+2^3+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)\)\(VT=2^{101}-1\)
\(VT=VP\)
8 tháng 8 2017
Thằng phúc chết tiệt, làm giúp ng` ta ko làm hết đuy, còn làm dở =))
Bài 2 :
a) Ta có :
\(3^{30}< 3^{34}\)
\(3^{30}=\left(3^3\right)^{10}=27^{10}\)
\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
Vì \(27^{10}>25^{10}\Leftrightarrow3^{30}>5^{20}\) (Mà \(3^{30}< 3^{34}\))
\(\Leftrightarrow5^{20}< 3^{34}\)
RG
0
= -2 + 30 -3 + 4-6457
= 28 - 3 + 4 -6457
= 29 - 6457
= -6448
1-3+30-3+4-6475
=28-3+4-6457
=25+4-6457
=29-6475
= -6446