Question

C=2+2^3+2^5+...+2^2013+2^2015

Answer 1

\(C=2+2^3+2^5+...+2^{2015}\)

\(\Rightarrow4C=2^3+2^5+2^7+...+2^{2017}\)

\(\Rightarrow4C-C=\left(2^3+2^5+2^7+...+2^{2017}\right)-\left(2+2^3+2^5+...+2^{2015}\right)\)

\(\Rightarrow3C=2^{2017}-2\)

\(\Rightarrow C=\frac{2^{2017}-2}{3}\)

Answer 2

\(C=2+2^3+2^5+...+2^{2013}+2^{2015}\)

\(4C=\left(4.2\right)+\left(4.2^3\right)+\left(4.2^5\right)+...+\left(4.2^{2013}\right)+\left(4.2^{2015}\right)\)

\(4C=2^3+2^5+2^7+...+2^{2015}+2^{2017}\)

\(4C-C=\left(2^3+2^5+2^7+...+2^{2013}+2^{2015}\right)-\left(2+2^3+2^5+...+2^{2015}+2^{2017}\right)\)

\(3C=2^{2017}-2\)

\(C=\frac{2^{2017}-2}{3}\)

Vậy \(C=\frac{2^{2017}-2}{3}\)

Answer 3

C = 2 + 2³ + 2⁵ + ... + 2²⁰¹³ + 2²⁰¹⁵

4C = 2³ + 2⁵ + 2⁷ + ... + 2²⁰¹⁵ + 2²⁰¹⁷

4C - C = (2³ + 2⁵ + 2⁷ + ... + 2²⁰¹⁵ + 2²⁰¹⁷) - (2 + 2³ + 2⁵ + ... + 2²⁰¹³ + 2²⁰¹⁵)

3C = 2²⁰¹⁷ - 2

\(C=\frac{2^{2017}-2}{3}\)