Question

rut gon 1+7^2+7^3+7^4+...+7^99

Answer 1

Đặt \(A=1+7^2+7^3+7^4+...+7^{99}\)

\(\Rightarrow7A=7\left(1+7^2+7^3+7^4+...+7^{99}\right)\)

\(\Rightarrow7A=7+7^3+7^4+7^5+...+7^{100}\)

\(\Rightarrow7A-A=\left(7+7^3+7^4+7^5+...+7^{100}\right)-\left(1+7^2+7^3+7^4+...+7^{99}\right)\)

\(\Rightarrow6A=7^{100}-1\)

\(\Rightarrow A=\frac{7^{100}-1}{6}\)

Answer 2

đặt S = 1 + 7² + 7³ + 7⁴ + .... + 7⁹⁹

=> 7S = 7 + 7³ + 7⁴ + 7⁵ + .... 7¹⁰⁰

=> 7S - S = (7 + 7³ + 7⁴ + 7⁵ + .... + 7¹⁰⁰) - (1 + 7² + 7³ + 7⁴ + .... + 7⁹⁹)

=> 6S = (7 + 7¹⁰⁰) - (1 + 7²) 

=> 6S = (7 - 1) + (7¹⁰⁰ - 7²)

=> 6S = 6 + 7¹⁰⁰ - 7²

=> S = \(\frac{6+7^{100}-7^2}{6}\)

Answer 3

rốt cuộc là ai đúng