Bài Mới Đây

[haukira]

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Tính
A= 4+2^2+2^3+2^4+...+2^99+2^100
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[hiensau99]

Tính
A= 4+2^2+2^3+2^4+...+2^99+2^100

Cách 1:
[TEX]A= 4+2^2+2^3+2^4+...+2^{99}+2^{100}[/TEX]
\Rightarrow[TEX]2A= 2^3+2^3+2^4+2^5+...+2^{100}+2^{101}[/TEX]
\Rightarrow[TEX]2A-A= (2^3+2^3+2^4+2^5+...+2^{100}+2^{101})-(4+2^2+2^3+2^4+...+2^{99}+2^{100})[/TEX]
\Rightarrow[TEX]A=2^3+2^3+2^4+2^5+...+2^{100}+2^{101}-4-2^2-2^3-2^4-...-2^{99}-2^{100}[/TEX]
\Rightarrow[TEX]A=2^3-4-2^2+2^{101}[/TEX]
\Rightarrow[TEX]A=2^{101}[/TEX]

Cách 2:
[TEX]A= 2^2+2^2+2^3+2^4+...+2^{99}+2^{100}[/TEX]
\Rightarrow[TEX]\frac{1}{2}A=2+2+2^2+2^3+...+2^{98}+2^{99}[/TEX]
\Rightarrow[TEX]A-\frac{1}{2}A=(2^2+2^2+2^3+2^4+...+2^{99}+2^{100})-(2+2+2^2+2^3+...+2^{98}+2^{99}) [/TEX]
\Rightarrow[TEX]\frac{1}{2}A=2^2+2^2+2^3+2^4+...+2^{99}+2^{100}-2-2-2^2-2^3-...-2^{98}-2^{99} [/TEX]
\Rightarrow[TEX]\frac{1}{2}A= 2^2-2-2+2^{100}[/TEX]
\Rightarrow[TEX]A= 2^{100}:\frac{1}{2}[/TEX]
\Rightarrow[TEX]A= 2^{101}[/TEX]

 

[yoyo2345]

A= 4+2^2+2^3+2^4+...+2^{99}+2^{100}
2A= 2^3+2^3+2^4+2^5+...+2^{100}+2^{101}
2A-A= (2^3+2^3+2^4+2^5+...+2^{100}+2^{101})-(4+2^2+2^3+2^4+...+2^{99}+2^{100})
A=2^3+2^3+2^4+2^5+...+2^{100}+2^{101}-4-2^2-2^3-2^4-...-2^{99}-2^{100}
A=2^3-4-2^2+2^{101}
A=2^{101}mình cũng hay làm thế

 

[duynhat123]

A= 4+2^2+2^3+2^4+...+2^{99}+2^{100}
2A= 2^3+2^3+2^4+2^5+...+2^{100}+2^{101}
2A-A= (2^3+2^3+2^4+2^5+...+2^{100}+2^{101})-(4+2^2+2^3+2^4+...+2^{99}+2^{100})
A=2^3+2^3+2^4+2^5+...+2^{100}+2^{101}-4-2^2-2^3-2^4-...-2^{99}-2^{100}
A=2^3-4-2^2+2^{101}
A=2^{101}mình cũng hay làm thế
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