Question

\(M=\frac{1+2+2^2+2^3+....+2^{2012}}{2^{2014}-2}\)

 

Tính M= ?

Answer 1

\(2M=\frac{2+2^2+2^3+...+2^{2013}}{2^{2014}-2}\)

\(2M-M=\frac{\left(2+2^2+...+2^{2013}\right)-\left(1+2^2+...+2^{2012}\right)}{2^{2014}-2}\)

\(M=\frac{1-2^{2013}}{2^{2014}-2}\)

Answer 2

Đặt A=1+2+2²+............+2²⁰¹²

2A=2+2²+2³+..............+2²⁰¹³

2A-A=2²⁰¹³-1

A=2²⁰¹³-1

=>M=\(\frac{2^{2013}-1}{2^{2014}-2}=\frac{2^{2013}-1}{2^{2013}.2-2}=\frac{2^{2013}-1}{2.\left(2^{2013}-1\right)}=\frac{1}{2}\)

Answer 3

m = m;m+1;m+2;.......