\(A=2^0+2^1+2^2+...+2^{20}\)

\(2A=2^1+2^2+2^3+...+2^{21}\)

\(A=2^{21}-1\)

Vậy \(A>B\)

\(-\frac{219}{220}< -\frac{215}{216}\)

Ta có:

\(1-\frac{-219}{220}=1\frac{219}{220}=1+\frac{219}{220}\)

\(1-\frac{-215}{216}=1\frac{215}{216}=1+\frac{215}{216}\)

Ta so sánh hai phân số \(\frac{219}{220};\frac{215}{216}\)

Ta có:

1-219/220=1/220

1-215/216=1/216

Vì 220>216 => 1/220 < 1/216 => 219/220 > 215/216 => 1+219/220 > 1+215/220 => \(-\frac{219}{220}>\frac{-215}{216}\)

Vậy \(-\frac{219}{220}>\frac{-215}{216}\)

Lời giải:

$B=\overline{4a,86}+\overline{8,b5}+\overline{18,9c}$

$=40,86+a+8,05+0,b+18,9+0,0c$

$=(40,86+8,05+18,9)+(a+0,b+0,0c)$

$=67,81+\overline{a,bc}< 68,5+\overline{a,bc}$

Vậy $B< A$

\(\dfrac{27}{86}\) < \(\dfrac{27}{81}\) = \(\dfrac{1}{3}\) = \(\dfrac{9}{27}\) < \(\dfrac{25}{27}\) 

Vậy \(\dfrac{27}{86}\) < \(\dfrac{25}{27}\) 

3⁸⁶=(3²)⁴³=9⁴³

2¹²⁹=(2³)⁴³=8⁴³

Vì: 9>8 nên: 3⁸⁶>2¹²⁹

bằng nhau nha

\(3^{86}=3^{43.2}=\left(3^2\right)^{43}=\)\(9^{43}\)

\(2^{129}=2^{3.43}=\left(2^3\right)^{43}=\)\(8^{43}\)

\(\Rightarrow9^{43}>8^{43}\Rightarrow3^{86}>2^{129}\)

P/s: Hoq chắc ạ