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A = 1.2 + 2.3 + ............ + 10.11
3A = 1.2.3 + 2.3.3 + .... + 10.11.3
3A = 1.2.(3-0) + 2.3.(4-1) +.......... + 10.11.(12 - 9)
3A = 1.2.3 + 2.3.4 - 1.2.3 + ............ + 10.11.12 - 9.10.11
3A = (1.2.3-1.2.3) + (2.3.4-2.3.4) +.......... + (9.10.11-9.10.11) + 10.11.12
3A = 10 . 11 . 12 = 1320
A = 1320 : 3 = 440
1: =72/90+65/90=137/90
2: =24/56-77/56=-53/56
3: =-7/10+4/5=1/10
4: =15/100-4/100=11/100
5: =4/6-5/6=-1/6
6: =10/40-15/40-76/40=-81/40
7: =-9/10+7/18
=-81/90+35/90=-46/90=-23/45
8: =27/90-55/90=-28/90=-14/45
9: =36/60-50/60-35/60=-49/60
10: =-4/9+5/6-3/8
=-32/72+60/72-27/72
=1/72
Đặt S = 1 x 2 + 2 x 3 + ..... + 9 x 10
3S = 1 x 2 x (3-0) + 2 x 3 x (4 - 1) + ....... + 9 x 10 x (11 - 8)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ......... + 9 x 10 x 11 - 8 x 9 x 10
3S = ( 1 x 2 x 3 -1 x 2 x 3) + ( 2 x 3 x4 - 2 x 3 x 4) + ..... + (8 x 9 x 10 - 8 x 9 x 10) + 9 x 10 x 11
3S = 9 x 10 x 11 = 990
S = 990 : 3 = 330
A = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... + 2005 + 2006 - 2007 - 2008 + 2009 + 2010 ( có 2010 số )
A = ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) + .... + ( 2005 + 2006 - 2007 - 2008 ) + ( 2009 + 2010 )
A = ( - 4 ) + ( - 4 ) + ... + ( - 4 ) + 4019 ( có 503 số )
A = ( - 4 ) . 502 + 4019
A = - 2008 + 4019
A = 2011.
CHÚC LÀM BÀI VUI VẺ
\(A=\left(4^5\times9^4+2\times6^9\right)\div\left(2^{10}\times3^8-6^8\times2\right)\)
\(\Leftrightarrow A=\frac{4^5\times9^4+2\times6^9}{2^{10}\times3^8-6^8\times2}\)
\(\Leftrightarrow A=\frac{\left(2^2\right)^5\times\left(3^2\right)^4+2\times\left(3\times2\right)^9}{2^{10}\times3^8-\left(3\times2\right)^8\times2}\)
\(\Leftrightarrow A=\frac{2^{10}\times3^8+2\times3^9\times2^9}{2^{10}\times3^8-3^8\times2^8\times2}\)
\(\Leftrightarrow A=\frac{2^{10}\times3^8+2^{10}\times3^8\times3}{2^{10}\times3^8-3^8\times2^9}\)
\(\Leftrightarrow A=\frac{3^8\left(2^{10}+2^{10}\times3\right)}{3^8\left(2^{10}-2^9\right)}\)
\(\Leftrightarrow A=\frac{2^{10}+2^{10}\times3}{2^{10}-2^9}\)
\(\Leftrightarrow A=\frac{2^{10}\left(1+3\right)}{2^9\left(2-1\right)}\)
\(\Leftrightarrow A=\frac{2\left(1+3\right)}{2-1}\)
\(\Leftrightarrow A=\frac{2\times4}{1}\)
\(\Leftrightarrow A=8\)
A= (45. 94+ 2. 69): (210. 38- 68. 2)
A= (210. 38+ 210.29): (210. 38- 38. 39)
A= [29. 38 (2+ 2. 3]: [29. 38(2- 1)]
A= (2+ 6): (2- 1)
A= 8: 1
A= 8
Vừa giải r :v