Question

Cho M = 5 + 5² + .... + 5¹⁰⁰

Tìm số tự nhiên n biết rằng : 4 x M + 5 = 5ⁿ

Answer 1

M = 5 + 5² + ... + 5¹⁰⁰

5M = 5² + 5³ + ... + 5¹⁰¹

5M - M = (5² + 5³ + ... + 5¹⁰¹) - (5 + 5² + ... + 5¹⁰⁰)

4M = 5¹⁰¹ - 5

4M + 5 = 5¹⁰¹ = 5ⁿ

=> n = 101

Vậy n = 101

Answer 2

\(M=5+5^2+...+5^{100}\)

\(5M=5^2+5^3+...+5^{101}\)

\(5M-M=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+...+5^{100}\right)\)

\(4M=5^{101}-5\)

\(4M+5=5^{101}-5+5\)

\(5^n=5^{101}\)

n = 101

Answer 3

Ta có:

\(M=5+5^2+...+5^{100}\)

\(\Rightarrow5M=5^2+5^3+...+5^{101}\)

\(\Rightarrow5M-M=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+...+5^{100}\right)\)

\(\Rightarrow4M=5^{101}-5\)

Mà \(4M+5=5^n\)

\(\Rightarrow5^{101}-5+5=5^n\)

\(\Rightarrow5^{101}=5^n\)

\(\Rightarrow n=101\)

Vậy n = 101

Answer 4

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