Question

D= 6+\(6^2\)+\(6^3\)+....+\(6^{100}\)

Answer 1

\(D=6+6^2+6^3+...+6^{100}\\ \Rightarrow6D=6^2+6^3+6^4...+6^{101}\\ \Rightarrow6D-D=\left(6^2+6^3+6^4...+6^{101}\right)-\left(6+6^2+6^3+...+6^{100}\right)\\ \Rightarrow5D=6^{101}-6\)

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

Answer 2

\(D=6+6^2+6^3+...+6^{100}\)

\(6D=6\left(6+6^2+6^3+...+6^{100}\right)\)

\(6D=6^2+6^3+6^4+...+6^{101}\)

\(6D-D=\left(6^2+6^3+6^4+...+6^{101}\right)-\left(6+6^2+6^3+...+6^{100}\right)\)

\(5D=6^{101}-6\)

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

Vậy \(D=\dfrac{6^{101}-6}{5}\)

 

 

Answer 3

Ta có: \(D=6+6^2+6^3+...+6^{100}\)

\(\Leftrightarrow6D=6^2+6^3+6^4+...+6^{101}\)

\(\Leftrightarrow5D=6^{101}-6\)

\(\Leftrightarrow D=\dfrac{6^{101}-6}{5}\)