Question

5^100 - 5^99 + 5^98 - 5^97 + ..... + 5^2 - 5

 

Answer 1

A = 5¹⁰⁰ - 5⁹⁹ + 5⁹⁸ - 5⁹⁷ + ... + 5² - 5

5A = 5¹⁰¹ - 5¹⁰⁰ + 5⁹⁹ - 5⁹⁸ + ... + 5³ - 5²

5A + A = 5¹⁰¹ - 5

6A = 5¹⁰¹ - 5

A = \(\dfrac{5^{101}-5}{6}\)

Answer 2

\(\text{Đặt }A=5^{100}-5^{99}+5^{98}-5^{97}+...+5^2-5\\5A=5^{101}-5^{100}+5^{99}-5^{98}+...+5^3-5^2\\5A+A=(5^{101}-5^{100}+5^{99}-5^{98}+...+5^3-5^2)+(5^{100}-5^{99}+5^{98}-5^{97}+...+5^2-5)\\\\6A=5^{101}-5\\\Rightarrow A=\frac{5^{101}-5}{6}\)

Answer 3

Đặt \(A=5^{100}-5^{99}+5^{98}-5^{97}+...+5^2-5\)

Ta có: \(5A=5^{101}-5^{100}+5^{99}-5^{98}+...+5^3-5^2\)

\(\Rightarrow5A+A=\left(5^{101}-5^{100}+5^{99}-5^{98}+...+5^3-5^2\right)+\left(5^{100}-5^{99}+5^{98}-5^{97}+...+5^2-5\right)\)

\(\Rightarrow6A=5^{101}-5\)

\(\Rightarrow A=\dfrac{5^{101}-5}{6}\)