\(3A=3+3^2+3^3+3^4+...+3^{21}\)

\(\Rightarrow2A=3A-A=3^{21}-1\)

\(\Rightarrow A=\frac{3^{21}-1}{2}\)

Do đó \(B-A=\frac{3^{21}}{2}-\frac{3^{21}-1}{2}=\frac{3^{21}-\left(3^{21}-1\right)}{2}=\frac{1}{2}\)

\(A=1+3+3^2+3^3+...+3^{20}\)

\(\Rightarrow3A=3+3^2+3^3+...+3^{21}\)

\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{21}\right)-\left(1+3+3^2+3^3+...+3^{20}\right)\)

\(\Rightarrow2A=3^{21}-1\)

\(\Rightarrow A=\frac{3^{21}-1}{2}=\frac{3^{21}}{2}-\frac{1}{2}\)

Ta lại có: 

\(B=\frac{3^{21}}{2}\)

\(\Rightarrow B-A=\left(\frac{3^{21}}{2}-\frac{1}{2}\right)-\frac{3^{21}}{2}=\frac{1}{2}\)

A = 1 + 3¹ + 3² + 3³ + ... + 3²⁰

3A = 3( 1 + 3¹ + 3² + 3³ + ... + 3²⁰ )

3A = 3 + 3² + 3³ + 3⁴ + ... + 3²¹

3A - A = ( 3 + 3² + 3³ + 3⁴ + ... + 3²¹ ) - ( 1 + 3¹ + 3² + 3³ + ... + 3²⁰ )

=> 2A = 3 + 3² + 3³ + 3⁴ + ... + 3²¹ - 1 - 3¹ - 3² - 3³ + ... - 3²⁰

2A = 2 + 3²¹

A = \(\frac{2+3^{21}}{2}\); B = \(\frac{3^{21}}{2}\)

Vì 2 + 3²¹ > 3²¹

=> \(\frac{2+3^{21}}{2}\)> \(\frac{3^{21}}{2}\)hay A > B 

A=1+ 3¹+3²+3³+...+3²⁰

3A = 3 + 3^2 + 3^3 + ... + 3^21

2A = 3^21 - 1

A = 3^21 - 1/2

3^21-1 < 3^21

=> 3^21-1/2 < 3^21/2

=> A < B

a: =18x941+18x59

=18(941+59)

=18x1000=18000

b: \(=81:27-16:8=3-2=1\)

c: =30-40+25=-10+25=15

d: =17(85+15)-150=1700-150=1550

e: =-150-180-200=-530

f: =17+15+40=72

Mình chỉ ghj đáp za thôj nên thông cảm nha

b)1953368

c)225

d)32

\(a,=4^{10}.4^{10}.4^{45}\)

    \(=4^{65}\)

\(b,=5^9+3^5\)

    \(=1953125+243\)

     \(=1953368\)

\(c,=1+8+27+64+125\)

    \(=225\)

\(d,=32^5:32^4\)

     \(=32\)

1. Tính tổng:

B = 2 - 4 - 6 + 8 + 10 - 12 - 14 + 16 + ... + 2002 - 2004 - 2006 + 2008

=> ( 2 - 4 - 6 + 8 )+ (10 - 12 - 14 + 16) + ... + (2002 - 2004 - 2006 + 2008)

=> (-8+ 8) +(-16+ 16) +.........+ ( -2008+ 2008)(1)

=> 0+0+...........+0

=> 0

Ta thấy (1) đều là những số đối nên kết quả đường nhiên bằng 0

\(A=1+4+4^2+4^3+...+4^{99}\\ \Rightarrow4A=4+4^2+4^3+...+4^{100}\\ \Rightarrow3.A=4^{100}-1\\ \Rightarrow A=\dfrac{4^{100}-1}{3}< \dfrac{4^{100}}{3}=\dfrac{B}{3}\\ \Rightarrow A< \dfrac{B}{3}\)