Ta có:

\(2^2S=2^2\left(2^2+2^4+....+2^{100}\right)\)

\(\Rightarrow4S=2^4+2^6+....+2^{102}\)

\(\Rightarrow4S-S=\left(2^4+2^6+....+2^{102}\right)-\left(2^2+2^4+....+2^{100}\right)\)

\(\Rightarrow3S=2^{100}-2^2=2^{100}-4\)

\(\Rightarrow S=\frac{2^{100}-4}{3}\)

a) Ta có: \(A=1+3+3^2+...+3^{99}+3^{100}\)

=> \(3A=3+3^2+3^3+...+3^{100}+3^{101}\)

=> \(3A-A=\left(3+3^2+...+3^{101}\right)-\left(1+3+...+3^{100}\right)\)

<=> \(2A=3^{101}-1\)

=> \(A=\frac{3^{101}-1}{2}\)

b) Ta có: \(B=1+4+4^2+...+4^{100}\)

=> \(4B=4+4^2+4^3+...+4^{101}\)

=> \(4B-B=\left(4+4^2+...+4^{101}\right)-\left(1+4+...+4^{100}\right)\)

<=> \(3B=4^{101}-1\)

=> \(B=\frac{4^{101}-1}{3}\)

Câu a:

A = 1+ 3 + 3^2+ ..+ 3^100

3A = 3 + 3^2+ 3^3 + ...+ 3^101

3A - A = 3 + 3^2+ 3^3 + ...+ 3^101 - (1+ 3 + 3^2+ ..+ 3^100)

2A = 3 + 3^2 + 3^3 + ...+ 3^100 - 1 - 3 - 3^2-..-3^100

2A = (3^101-1)+(3^2-3^2)+..+(3^100-3^100)

2A = 3^101 - 1 + 0 + 0+ ...+ 0

2A = 3^101 - 1

A = (3^101 - 1)/2

Câu b:

A = 1+ 4 + 4^2+ ..+ 4^100

4A = 4 + 4^2+ 4^3 + ...+ 4^101

4A - A = 4 + 4^2+ 4^3 + ...+ 4^101 - (1+ 4 + 4^2+ ..+ 4^100)

4A - A= =4 + 4^2 + 4^3 + ...+ 4^100 - 1 - 4 - 4^2-..-4^100

3A = (4^101-1)+(4^2-4^2)+..+(4^100-4^100)

3A = 4^101 - 1 + 0 + 0+ ...+ 0

3A = 4^101 - 1

A = (4^101 - 1)/3

B = 1+4+4²+4³+...+4¹⁰⁰

4B= 4+4²+4³+4⁴+....+4¹⁰¹

4B-B= 4+4²+4³+4⁴+....+4^{101 -}1-4-4²- 4³-...- 4¹⁰⁰

3B = 4¹⁰¹ - 1

  B  = \(\frac{4^{101}-1}{3}\)

B x 4=4+4²+4³+4⁴+............+4¹⁰⁰

B X 4 - 4=(4+4²+4³+4⁴+.......+4¹⁰⁰+4¹⁰¹) - (1+4¹+4²+4³+4⁴+..............+4¹⁰⁰)

=>B=4¹⁰¹ – 1

k hộ mình nha

Câu a:

A = 2 + 2^2+ 2^3 +..+ 2^100

2A = 2^2 + 2^3 + ..+ 2^101

2A - A = 2^2 + 2^3 + ..+ 2^101 - (2 + 2^2+ 2^3 +..+ 2^100)

A = 2^2 + 2^3 + ... + 2^101 - 2 - 2^2 - 2^3 -...-2^100

A = (2^101 - 2) + (2^2 - 2^2) + (2^3 -2^3) + ...+ (2^100 - 2^100)

A = 2^101 - 2 + 0 + 0 + ...+ 0

A = 2^101 - 2

Câu b:

B = 4+ 4^2 + 4^3 + ...+ 4^n

4B = 4^2 + 4^3 + ..+ 4^n+1

4B - B = 4^2 + 4^3 + ..+ 4^n+1-(4+ 4^2 + 4^3 + ...+ 4^n)

3B = 4^2 + 4^3 + ..+ 4^n+1 - 4 - 4^2 - 4^3 - ...- 4^n

3B = (4^n+1- 4) + (4^2 -4^2)+..+(4^n-4^n)

3B = 4^n+1- 4 + 0 + 0

3B = 4^n+1 - 4

B = (4^n+1 - 4)/3

bằng shit trâu

\(4E=2^2.E=2^2+2^4+2^6+...+2^{2020}\)

\(3E=4E-E=2^{2020}-1\Rightarrow E=\frac{2^{2020}-1}{3}\)

\(3F=3^2+3^3+3^4+...+3^{101}\)

\(2F=3F-F=3^{101}-3\Rightarrow F=\frac{3^{101}-3}{2}\)

bài A và B nè bạn!

A=1+3+3²+...+3¹⁰⁰

3A=3+3²+3³+...+3¹⁰¹

=>3A+1=1+3+3²+...+3¹⁰⁰+3¹⁰¹=A+3¹⁰¹

=>3A-A=3¹⁰¹-1

2A=3¹⁰¹-1

A=(3¹⁰¹-1)/2

B=1+4+4²+...+4⁵⁰

4B=4+4²+...+4⁵¹

4B+1=1+4+4²+...+4⁵⁰+4⁵¹=B+4⁵¹

=>4B-B=4⁵¹-1

3B=4⁵¹-1

B=(4⁵¹-1)/3

\(S=2+2^2+2^3+....+2^{100}\)

\(\Rightarrow2S=2^2+2^3+....+2^{101}\)

\(\Rightarrow S=2^{101}-2\)

\(S=2^1+2^2+...+2^{99}+2^{100}\)

\(\Leftrightarrow2S=2^2+...+2^{101}\)

\(\Leftrightarrow S=2^{101}-2\)

Tên bạn là gì trả lời đúng rùi đó