Question

[buikhanhphuong]

thực hiện phép tính: 

N = 1+2²+2³+.........2²⁰¹²

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            2²⁰¹⁴-2

Answer 1

[VICTORY_ Trần Thạch Thảo]

\(N=1+2^2+2^3+...+2^{2012}\)

\(\Rightarrow2N=2.\left(1+2^2+2^3+...+2^{2012}\right)\)

\(\Rightarrow2N=2+2^2+2^3+2^4+....+2^{2013}\)

\(\Rightarrow2N=1+2+2^2+2^3+....+2^{2012}+2^{2013}-1\)

\(\Rightarrow2N=N+2^{2013}-1\)

\(\Rightarrow N=2^{2013}-1\)

\(\Rightarrow\)2²⁰¹³-1

     2²⁰¹⁴-2

= 1

Answer 2

[Lelouch vi Britannia]

\(2N=2+2^3+2^4+...+2^{2013}\)

\(2N-N=\left(2+2^3+2^4+...+2^{2013}\right)-\left(1+2^2+2^3+...+2^{2012}\right)\)\(N=2+2^{2013}-\left(1+2^2\right)\)

\(=2^{2013}+2-5=2^{2013}-3\)