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

\(\Rightarrow2S=2-2^2+2^3-2^4+...+2^{2013}-2^{2014}\)

\(\Rightarrow2S+S=2-2^2+2^3-...-2^{2014}+1-2^2-2^3+...-2^{2013}\)

\(\Rightarrow3S=1-2^{2014}\)\(\Rightarrow3S-2^{2014}=1-2^{2015}\)

[(2³ - 5) . (-3)+9] . (2²⁰¹² . 2011 - 2012² . 2011+1)

= [ 3 . ( -3 ) + 9] . (2²⁰¹² . 2011 - 2012² . 2011+1)

=  [ (-9) + 9 ] . (2²⁰¹² . 2011 - 2012² . 2011+1)

= 0 . (2²⁰¹² . 2011 - 2012² . 2011+1)

= 0

[ (2³ - 5) . (-3) + 9 ] . ( 2²⁰¹² . 2011 - 2012² . 2011+1 )

= [ 3 . ( -3 ) + 9] . (2²⁰¹² . 2011 - 2012² . 2011+1 )

= 0 . (2²⁰¹² . 2011 - 2012² . 2011+1) = 0

Đặt N = 1 + 2 + 2² +...+ 2²⁰¹²

2N = 2 + 2² + 2³ +...+ 2²⁰¹³

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

N = 2²⁰¹³ - 1

Thay N vào M ta được:

Đặt \(N=1+2+2^2+...+2^{2012}\)

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

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

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

Thay N vào M ta được:

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

Sửa đề: \(M=\frac{1+2+2^2+\cdots+2^{2012}}{2^{2014}-2}\)

Đặt \(A=1+2+2^2+\cdots+2^{2012}\)

=>\(2A=2+2^2+2^3+\cdots+2^{2013}\)

=>2A-A=\(2+2^2+2^3+\cdots+2^{2013}-1-2-2^2-\cdots-2^{2012}\)

=>\(A=2^{2013}-1\)

Ta có: \(M=\frac{1+2+2^2+\cdots+2^{2012}}{2^{2014}-2}\)

\(=\frac{2^{2013}-1}{2\left(2^{2013}-1\right)}=\frac12\)

a) x lớn hơn 120

b) x=8

2) a) 2002/2001 lớn hơn

b) 2015/2018 lớn hơn

c) 27/37 lớn hơn

Đúng thì like giúp mik nha. Thx bạn

bạn có chs tiktok ko

a, \(\dfrac{7}{22}\) - \(\dfrac{15}{23}\) + \(\dfrac{2022}{2023}\) - \(\dfrac{8}{23}\) + \(\dfrac{15}{22}\)

= ( \(\dfrac{7}{22}\) + \(\dfrac{15}{22}\)) - ( \(\dfrac{15}{23}+\dfrac{18}{23}\)) + \(\dfrac{2022}{2023}\)

= \(\dfrac{22}{22}\) - \(\dfrac{23}{23}\) + \(\dfrac{2022}{2023}\)

= 1 - 1 + \(\dfrac{2022}{2023}\)

= \(\dfrac{2022}{2023}\) 

b, - \(\dfrac{2}{11}\) + 5\(\dfrac{5}{6}\) ( 14\(\dfrac{1}{5}\) - 11\(\dfrac{1}{5}\)): 5\(\dfrac{1}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) ( \(\dfrac{71}{5}\) - \(\dfrac{56}{5}\)) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) . \(\dfrac{15}{5}\) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{2}\) \(\times\) \(\dfrac{2}{11}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{11}\)

= \(\dfrac{33}{11}\)

= 3 

c, 2000 + { 20 - [ 4.2022⁰ - (3² + 5):2] }

= 2000 + { 20 - [ 4.1 - (9+5):2]}

= 2000 + { 20 - [ 4 - 14 : 2 ]}

= 2000 + { 20 - [ 4 -7]}

= 2000 + { 20 - (-3)}

= 2000 + 23

= 2023

a: \(\frac{7}{22}+\frac{-15}{23}+\frac{2022}{2023}+\frac{-8}{23}+\frac{15}{22}\)

\(=\left(\frac{7}{22}+\frac{15}{22}\right)+\left(-\frac{15}{23}-\frac{8}{23}\right)+\frac{2022}{2023}\)

\(=1-1+\frac{2022}{2023}=\frac{2022}{2023}\)

b: \(-\frac{2}{11}+5\frac56\left(14\frac15-11\frac15\right):5\frac12\)

\(=-\frac{2}{11}+\frac{35}{6}\left(14+\frac15-11-\frac15\right):\frac{11}{2}\)

\(=\frac{-2}{11}+\frac{35}{6}\cdot\frac{2}{11}\cdot3=\frac{-2}{11}+\frac{35}{11}=\frac{33}{11}=3\)

c: \(2000+\left\lbrace20-\left\lbrack4\cdot2022^0-\left(3^2+5\right):2\right\rbrack\right\rbrace\)

\(=2000+20-\left\lbrack4\cdot1-14:2\right\rbrack\)

=2020-(4-7)

=2020-(-3)

=2023

hình như đề bài sai thì pải

a) phải là 2²⁵-2²⁴+2²³ và 2²³-2²²+2²¹ mới đúng

Đặt \(A=2^{2013}+2^{2012}+\cdots+2^3+2^2+3\)

=>\(A=2^{2013}+2^{2012}+\cdots+2^2+2+1\)

=>\(2A=2^{2014}+2^{2013}+\cdots+2^3+2^2+2\)

=>\(2A-A=2^{2014}+2^{2013}+\cdots+2^3+2^2+2-2^{2013}-2^{2012}-\cdots-2^2-2-1\)

=>\(A=2^{2014}-1\)

Ta có: \(B=2^{2014}-2^{2013}-2^{2012}-\cdots-2^3-2^2-3\)

=>\(B=2^{2014}-\left(2^{2014}-1\right)\)

\(=2^{2014}-2^{2014}+1=1\)