2^2+2^3+2^4+...+2^123
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= (2 x 4) + (123 x 4) x 4
= 8 + 492 x 4
= 8 + 1968
= 1976
Tính nhanh
a) 72. (-50).(-2).(-2)
b) 125.(-5).(-20).8
c) 125.(-3).(-32).(-4)
d) (-123 – 123-123-123).125
Lời giải:
a)
\(A=75^2+50.75+25^2=75^2+2.25.75+25^2\)
\(=(75+25)^2=100^2=10000\)
b) \(123^2+23^2-46.123=123^2-2.23.123+23^2\)
\(=(123-23)^2=100^2=10000\)
c) \((3^4-1)(3^4+1)-9^4\)
\(=[(3^4)^2-1^2]-9^4=(9^4-1)-9^4=-1\)
(1/2+2/3+3/4+4/5+...+122/123+123/124).(125-5.25)
=(1/2+2/3+3/4+4/5+...+122/123+123/124).(125-125)
=(1/2+2/3+3/4+4/5+...+122/123+123/124).0=0
a,123*3+1234*4-123
=369+4936-123
=5182
b,1457*4+1236*2-1236
=5828+2472-1236
=7064
c,214*4+456*2+46
=856+912+46
=1814
tick nha !!!
a) \(=\frac{3}{17}-\frac{2}{345}+\frac{5}{12}+\frac{2}{345}-\frac{3}{17}+\frac{1}{12}\)
\(=\left(\frac{3}{17}-\frac{3}{17}\right)+\left(\frac{2}{345}-\frac{2}{345}\right)+\left(\frac{5}{12}+\frac{1}{12}\right)\)
\(=\frac{6}{12}=\frac{1}{2}\)
b) \(=-\frac{49}{25}-\frac{5}{36}+\frac{4}{123}+\frac{49}{25}-\frac{4}{123}-\frac{1}{36}\)
\(=\left(-\frac{49}{25}+\frac{49}{25}\right)+\left(\frac{4}{123}-\frac{4}{123}\right)-\left(\frac{5}{36}+\frac{1}{36}\right)\)
\(=-\frac{6}{36}=-\frac{1}{6}\)
2/5 x 1/2 : 1/3 = 1/5 : 1/3
= 3/5
2/9 : 2/3 x 1/2 = 1/3 x 1/2
= 1/6
2/7 : 2/3 - 1/7 = 3/7 - 1/7
= 2/7
1/2 x 1/3 + 1/4 = 1/6 + 1/4
= 5/12
5535 : 123 = 45 ; 6560 : 234 = 28 ( dư 8 ) ; 32076 : 123 = 260 ( dư 96 )
Đặt \(A=2^2+2^3+2^4+...+2^{123}\)
\(2A=2^3+2^4+2^5+...+2^{124}\)
\(2A-A=\left(2^3+2^4+2^5+...+2^{124}\right)-\left(2^2+2^3+2^4+...+2^{123}\right)\)
\(A=2^{124}-4\)
\(A=2^2+2^3+2^4+...+2^{123}\)
\(2\cdot A=2^3+2^4+2^5+...+2^{124}\)
\(A=2^{124}-2^2=2^{124}-4\)