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2) \(A=2+2^2+2^3+2^4+...+2^{10}\)
\(2A=2^2+2^3+2^4+...+2^{11}\) . Mà 2A - A =A nên:
\(A=\left(2^2+2^3+2^4+...2^{11}\right)-\left(2+2^2+2^3+2^4+...+2^{10}\right)\) hay
\(A=2^{11}-2\Leftrightarrow A+2=2^{11}^{^{\left(đpcm\right)}}\)
A = 2^3 + 4^3 + 6^3 + ...+ 18^3
A = (1.2)^3 + (2.2)^3 + (2.3)^3 + ... + (2.9)^3
A = 1^3.2^3 + 2^3.2^3 + 2^3.3^3 + ... + 2^3.9^3
A = 2^3.(1^3 + 2^3 + ... + 9^3)
A = 2^3.2025
A = 8.2025
A = 16200
A = 2\(^3\) + 4\(^3\) + 6\(^3\) + ...+ 18\(^3\)
A = (1.2)\(^3\) + (2.2)\(^3\) + (2.3)\(^3\) + ... + (2.9)\(^3\)
A = 1\(^3\).2\(^3\) + 2\(^3\).2\(^3\) + 2\(^3\).3\(^3\) + ... + 2\(^3\).9\(^3\)
A = 2\(^3\).(1\(^3\) + 2\(^3\) + ... + 9\(^3\))
A = 2\(^3\).2025
A = 8.2025
A = 16200
A = 2 + 2\(^2\) + 2\(^3\) + 2\(^4\) + ... + 2\(^{10}\)
2A = 2\(^2\) + 2\(^3\) + 2\(^4\) + ...+ 2\(^{10}\) + 2\(^{11}\)
2A - A = 2\(^2\) + 2\(^3\) + 2\(^4\) + ...+ 2\(^{10}\) + 2\(^{11}\) - ( 2 + 2\(^2\) + 2\(^3\) + 2\(^4\) + ... + 2\(^{10}\) )
A = 2\(^2\) + 2\(^3\) + 2\(^4\) + ...+ 2\(^{10}\) + 2\(^{11}\) - 2 - 2\(^2\) -...-2\(^{10}\)
A = (2\(^2\) - 2\(^2\)) + (2\(^3\) - 2\(^3\)) + ... + (2\(^{10}\) - 2\(^{10}\)) + (2\(^{11}\) - 2)
A = 0 + 0 + ... + 0 + 2\(^{11}\) - 2
A + 2 = 2\(^{11}\) - 2 + 2
A + 2 = 2\(^{11}\) - (2 - 2)
A + 2 = 2\(^{11}\) - 0
A + 2 = 2\(^{11}\) (đpcm)
S = 22 + 42 + 62 + ... + 202
= (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2
= 22.12 + 22.22 + 22.32 + ... + 22.102
= 22 (12 + 22 + ... + 102 )
= 4 . 385 = 1540
A = 2\(^3\) + 4\(^3\) + 6\(^3\) + ...+ 18\(^3\)
A = (1.2)\(^3\) + (2.2)\(^3\) + (2.3)\(^3\) + ... + (2.9)\(^3\)
A = 1\(^3\).2\(^3\) + 2\(^3\).2\(^3\) + 2\(^3\).3\(^3\) + ... + 2\(^3\).9\(^3\)
A = 2\(^3\).(1\(^3\) + 2\(^3\) + ... + 9\(^3\))
A = 2\(^3\).2025
A = 8.2025
A = 16200
a,\(A=2^{200}-2^{199}-2^{198}-...-2-1\)
\(2A=2^{201}-2^{200}-...-2^2-2\)
\(2A-A=A=2^{101}+1\)
b,\(b=2^3+4^3+...+20^3\)
\(b=2^3\left(1^3+2^3+...+10^3\right)\)
\(b=8.2025\)
\(b=16200\)
Ta có: 1^2 + 2^2 + ...+10^2 = 385
=> 4(1^2 + 2^2 +...+10^2) = 1540
=> 2^2 + 4^2 + ... + 20^2 = 1540
Nhấn đúng cho mk nha!!!!!!!!!!!!
ta có: 23+43+63+...+183=(2.1)3+(2.2)3+(2.3)3+...+(2.9)3
=23.13+23.23+23.33+...+23.93
=8.(13+23+33+....+93)
= 8.2025
= 16200
S=\(2^2+4^2+....+20^2\)
\(S=2^2.1^2+2^2.2^2+2^2.3^2+.....+2^2.10^2\)
S=\(2^2\left(1^2+2^2+...+10^2\right)\)
S=4.385=1540
câu b tương tự