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Tui cần gấp
Đúng tui k nhưng làm hẳn ra nha :)
Nếu lâu thì làm mẫu 1 vài phần OK :)
a) \(2A=2^1+2^2+2^3+...+2^{2010}\)
=> \(2A-A=2^{2011}-2^0\Leftrightarrow A=2^{2011}-1\)
b) \(3B=3+3^2+3^3+3^4+...+3^{101}\)
=> \(3B-B=3^{101}-1\Leftrightarrow2B=3^{101}-1\Leftrightarrow B=\frac{1}{2}\left(3^{101}-1\right)\)
Tương tự Cx4, Dx5
A = 20 + 21 + 22 + ... + 22006
2A = 2 + 22 + 23 +...+ 22006 + 22007
2A - A = ( 2 + 22 + 23 + ... + 22006 + 22007 ) - ( 20 + 21 + 22 +...+ 22006 )
A = 22007 - 1
Ta có : A = 1 + 2 + 3 + ... + 2008
\(A=\frac{\left(2008+1\right)\left[\left(2008-1\right)\div1+1\right]}{2}\)
\(A=\frac{2009.2008}{2}\)
\(A=2017036\)
Ta có: B = 1 + 2 + 3 + ... + 1010
\(B=\frac{\left(1010+1\right)\left[\left(1010-1\right):1+1\right]}{2}\)
\(B=\frac{1011.1010}{2}\)
\(B=510555\)
\(A=1+2+3+4+5+...+2008\)
\(A=\left(2008+1\right)\left(\left(2008-1\right):1+1\right):2=2009.2008:2\)
\(=2009.1004=2017036\)
\(B=1+2+3+4+...+1010\)
\(B=\left(1010+1\right)\left(\left(1010-1\right):1+1\right):2=1011.\left(1010:2\right)\)
\(=1011.505=510555\)
\(C=2+5+8+11+...+302\)
\(C=\left(302+2\right)\left(\left(302-2\right):3+1\right):2=304.101:2\)
\(=15352\)
\(D=3+3^2+3^3+3^4+...+3^{2019}\)
\(3D=3^2+3^3+3^4+...+3^{2020}\)
\(3D-D=\left(3^2+3^3+3^4+...+3^{2020}\right)-\left(3+3^2+3^3+3^4+...+3^{2019}\right)\)
\(2D=3^{2020}-3\)
\(\Rightarrow D=\frac{3^{2020}-3}{2}\)
\(E=4^{10}+4^{11}+4^{12}+...+4^{100}\)
\(4E=4^{11}+4^{12}+4^{13}+...+4^{101}\)
\(4E-E=\left(4^{11}+4^{12}+4^{13}+...+4^{101}\right)-\left(4^{10}+4^{11}+4^{12}+...+4^{100}\right)\)
\(3E=4^{101}-4^{10}\)
\(E=\frac{4^{101}-4^{10}}{3}\)
a) Ta có : A = 1 + 2 + 22 + ..... + 22015
=> 2A = 2 + 22 + ..... + 22016
=> 2A - A = 22016 - 1
=> A = 22016 - 1
b) Ta có : B = 311 + 312 + 313 + ..... + 3101
=> 3B = 312 + 313 + ..... + 3102
=> 3B - B = 3102 - 311
=> 2B = 3102 - 311
=> B = \(\frac{3^{102}-3^{11}}{2}\)
a, ta có : 3A = 3 + 32 + 33 + ... + 3101
3A - A = ( 3+32 + 33+...+3101) - (1 + 3 + 32 + ... + 3100)
2A = 3101 - 1
A = (3101 - 1) : 2
tương tự tính b,c bạn nhé
*) A=2+22+23+24+....+2100
<=> 2A=22+23+24+....+2101
<=> A=2101-2
*) B=1+3+32+33+....+32009
<=> 3B=3+32+33+34+....+32010
<=> 2B=32010-3
<=> \(B=\frac{3^{2010}-3}{2}\)
*) C=1+5+52+53+....+51998
<=> 5C=5+52+53+54+....+51999
<=> 4C=51999-5
<=> \(C=\frac{5^{1999}-5}{4}\)
*) D=4+42+43+....+4n
<=> 4D=42+43+44+....+4n+1
<=> 3D=4n+1-4
<=> D=\(\frac{4^{n+1}-4}{3}\)