Question

rút gọn

\(1-3+3^2-3^3+........-3^{99}+3^{100}\)

bài khó quá giải giúp mihf nếu đúng mình tik cho nhé

Answer 1

giải luôn nha

 

Answer 2

Đặt \(A=1-3+3^2-3^3+...-3^{99}+3^{100}\)

\(\Rightarrow3A=3-3^2+3^3-...-3^{100}+3^{101}\)

\(\Rightarrow3A+A=3-3^2+3^3-...-3^{100}+3^{101}+1-3+3^2-3^3+...-3^{99}+3^{100}\)

\(\Rightarrow4A=1+3^{101}\)

\(\Rightarrow A=\dfrac{1+3^{101}}{4}\)

Answer 3

Ta có: \(A=1-3+3^2-3^3+...-3^{99}+3^{100}\)

\(\Leftrightarrow3\cdot A=3-3^2+3^3-3^4+...-3^{100}+3^{101}\)

\(\Leftrightarrow4\cdot A=3^{101}+1\)

hay \(A=\dfrac{3^{101}+1}{4}\)