Question

C = 4 + 4 mũ 2 + 4 mũ 3 + ... + 4 mũ n

Answer 1

C=4 + 4² + 4³ +....+ 4ⁿ

=> C= \(4^1+4^2+4^3+...+4^n\)

=>4C = 4. ( 4¹+4²+4³+...+4ⁿ)

=>4C = 4²+4³+4⁴+....+4ⁿ⁺¹

=>4C-C = (4²+4³+4⁴+....+4ⁿ⁺¹)-(4¹+4²+4³+....+4ⁿ)

=>3C=4ⁿ⁺¹-4¹

=>3C=4ⁿ⁺¹-4

=>C=\(\frac{4^{n+1}-4}{3}\)

Answer 2

\(C=4+4^2+4^3+...+4^n\)

\(\Rightarrow C=4^2+4^3+4^4+...+4^{n+1}\)

\(\Rightarrow C=4^2+4^3+4^4+...+4^{n+1}\)

\(\Rightarrow4C-C=4^{n+1}-4\)

\(\Rightarrow3C=4^{n+1}-4^1\)

\(\Rightarrow C=\frac{4^{n+1}-4^1}{3}\)