Question

[dương nguyễn quỳnh anh]

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

Answer 1

[Kiệt Nguyễn]

\(A=2+2^2+2^3+...+2^{99}+2^{100}\)

\(\Rightarrow2A=2^2+2^3+2^4+...+2^{100}+2^{101}\)

\(\Rightarrow A=2^{101}-2\)

\(\Rightarrow A+2=2^{101}-2+2\)

\(\Rightarrow A+2=2^{101}\)

Answer 2

[Funimation]

\(A=2+2^2+2^3+...+2^{100}\)

\(\Rightarrow2A=2.\left(2+2^2+2^3+...+2^{100}\right)\)

\(\Rightarrow2A=2^2+2^3+2^4+...+2^{101}\)

\(\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)

\(\Rightarrow A=2^{101}-2\)

\(\Rightarrow A+1=2^{101}-2+2\)

\(\Rightarrow A+2=2^{101}\)

Vậy A+2=2¹⁰¹