Question

M=1+2+2²+2³+....+2²⁰¹²/2²⁰¹⁴-2

giải jup mik nhé ^^

dấu (  /  ) là ps nhé

Answer 1

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

đặt \(A=1+2+2^2+2^3+...+2^{2012}\)   

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

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

\(A=2^{2013}-1\)   (2)

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

\(=\frac{2^{2013}-1}{2^{2013}\cdot2-1\cdot2}\)

\(=\frac{2^{2013}-1}{2\left(2^{2013}-1\right)}\)

\(=\frac{1}{2}\)

Answer 2

Tách tử và mẫu ta có:

Đặt A = 1 + 2 + 2² + 2³ + .......... + 2²⁰¹²

2A = 2 + 2² + 2³ + 2⁴ + ............ + 2²⁰¹³

2A - A = ( 2 + 2² + 2³ + 2⁴ + ............ + 2²⁰¹³ ) - ( 1 + 2 + 2² + 2³ + ............. + 2²⁰¹² )

A = 2²⁰¹³ - 1

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

\(\Rightarrow M=\frac{1}{2}\)