A=1+3+3^2+3^3+3^4+3^5+3^6+3^7 chung minh A=(3^8-1):2
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a) A=21+22+23+...+22010
A=(21+22)+(23+24)+.....+(22009+22010)
A=(21x3)+(23x3)+.....+(22009x3)
A=3x(21+23+.......+22009)
Vậy A chia hết cho 3.
NHỮNG CÂU CÒN LẠI BẠN LÀM TƯƠNG TỰ !
A= 3( 1+3+3^2+3^3+3^4+3^5+3^6+3^7+3^8) chia hết cho 3
a: \(=\dfrac{4}{9}\left(4+\dfrac{1}{3}+13+\dfrac{2}{3}\right)=\dfrac{4}{9}\cdot18=8\)
b: \(=\dfrac{3}{8}\left(5+\dfrac{1}{4}+10+\dfrac{3}{4}\right)=\dfrac{3}{8}\cdot16=6\)
c: \(=\dfrac{-2}{7}\left(6+\dfrac{1}{5}+14+\dfrac{4}{5}\right)=\dfrac{-2}{7}\cdot21=-6\)
a) \(4\dfrac{3}{8}+5\dfrac{2}{3}\)
\(=\dfrac{35}{8}+\dfrac{17}{3}\)
\(=\dfrac{105}{24}+\dfrac{136}{24}\)
\(=\dfrac{241}{24}\)
b) \(2\dfrac{3}{8}+1\dfrac{1}{4}+3\dfrac{6}{7}\)
\(=\dfrac{19}{8}+\dfrac{5}{4}+\dfrac{27}{7}\)
\(=\dfrac{29}{8}+\dfrac{27}{7}\)
\(=\dfrac{419}{56}\)
c) \(2\dfrac{3}{8}-1\dfrac{1}{4}+5\dfrac{1}{3}\)
\(=\dfrac{19}{8}-\dfrac{5}{4}+\dfrac{16}{3}\)
\(=\dfrac{9}{8}+\dfrac{16}{3}\)
\(=\dfrac{155}{24}\)
d) \(\left(\dfrac{5}{2}+\dfrac{1}{3}\right):\left(1-\dfrac{1}{2}\right)\)
\(=\dfrac{17}{6}:\dfrac{1}{2}\)
\(=\dfrac{17}{6}\cdot2\)
\(=\dfrac{17}{3}\)
e) \(\left(\dfrac{5}{2}-\dfrac{1}{3}\right)\cdot\dfrac{9}{2}-\dfrac{6}{7}\)
\(=\dfrac{13}{6}\cdot\dfrac{9}{2}-\dfrac{6}{7}\)
\(=\dfrac{39}{4}-\dfrac{6}{7}\)
\(=\dfrac{249}{28}\)
a: =4+3/8+5+2/3
=9+9/24+16/24
=9+25/24
=216/24+25/24=241/24
b: \(=\dfrac{19}{8}+\dfrac{5}{4}+\dfrac{27}{7}=\dfrac{19+10}{8}+\dfrac{27}{7}\)
=27/7+29/8
=419/56
c: =2+3/8-1-1/4+5+1/3
=6+3/8-1/4+1/3
=6+3/8+1/12
=144/24+9/24+2/24
=155/24
d: =(15/6+2/6):1/2
=17/6*2
=17/3
e: =(15/6-2/6)*9/2-6/7
=13/6*9/2-6/7
=117/12-6/7
=249/28
\(4A=4+4^2+4^3+4^4+4^5+4^6+4^7\\ 4A-A=4^7-1\\ 3A=4^7-1\\ A=\dfrac{4^7-1}{3}44\)
viết lại đề đi bạn
\(A=1+3+...+3^7\\ \Rightarrow3A=3+3^2+...+3^8\\ \Rightarrow3A-A=\left(3+3^2+...+3^8\right)-\left(1+3+...+3^7\right)\\ \Rightarrow2A=3^8-1\\ \Rightarrow A=\dfrac{3^8-1}{2}\)