Question

cho A=3+3^2+3^3+..................+3^100

Tìm số tự nhiên n biết 2A+3=3^n

Answer 1

Ta có \(A=3+3^2+3^3+...+3^{100}\)

\(\Rightarrow3A=3^2+3^3+3^4+...+3^{101}\)

\(\Rightarrow3A-A=3^{101}-3\)

\(2A=3^{101}-3\)

Ta có \(2A+3=3^n\)

hay \(3^{101}-3+3=3^n\)

\(3^{101}=3^n\)

\(n=101\)

Answer 2

A=3+3²+3³+.....+3¹⁰⁰

3a=3.(3+3²+3³+....+3¹⁰⁰)

3A=3²+3³+3⁴+....+3¹⁰¹

3A-A=(3²+3³+3⁴+....+3¹⁰¹)-(3+3²+3³+.....+3¹⁰⁰)

2A=3¹⁰¹-3

2A+3=3¹⁰¹-3+3

2A+3=3¹⁰¹

3ⁿ=3¹⁰¹

=>n\(\in\)(101)

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