Câu hỏi của dương nguyễn quỳnh anh

Question

cho A =2+22+23+...+2100.hãy viết A +2 dưới dạng một lũy thừa

Kiệt Nguyễn · Accepted Answer

$A=2+2^2+2^3+...+2^{99}+2^{100}$$\Rightarrow2A=2^2+2^3+2^4+...+2^{100}+2^{101}$$\Rightarrow A=2^{101}-2$$\Rightarrow A+2=2^{101}-2+2$$\Rightarrow A+2=2^{101}$Câu trả lời: $A=2+2^2+2^3+...+2^{99}+2^{100}$$\Rightarrow2A=2^2+2^3+2^4+...+2^{100}+2^{101}$$\Rightarrow A=2^{101}-2$$\Rightarrow A+2=2^{101}-2+2$$\Rightarrow A+2=2^{101}$

Funimation · Answer

$A=2+2^2+2^3+...+2^{100}$$\Rightarrow2A=2.\left(2+2^2+2^3+...+2^{100}\right)$$\Rightarrow2A=2^2+2^3+2^4+...+2^{101}$$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)$$\Rightarrow A=2^{101}-2$$\Rightarrow A+1=2^{101}-2+2$$\Rightarrow A+2=2^{101}$Vậy A+2=2101Câu trả lời: $A=2+2^2+2^3+...+2^{100}$$\Rightarrow2A=2.\left(2+2^2+2^3+...+2^{100}\right)$$\Rightarrow2A=2^2+2^3+2^4+...+2^{101}$$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)$$\Rightarrow A=2^{101}-2$$\Rightarrow A+1=2^{101}-2+2$$\Rightarrow A+2=2^{101}$Vậy A+2=2101

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