A = 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90 

2A = 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100

2A - A = ( 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100 ) - (  2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90 ) 

A = 2^100 - 2^3 

B = 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50 

5B = 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51 

5B - B = ( 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51 ) - ( 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50 )

4B = 5^51 - 1 

B = 5^51 - 1 / 4

a) 3A = 3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (1 + 3 + 3 ^2 + 3 ^ 3 + ... + 3 ^100)
=> 2A = 3^101 - 1 => A = (3^101 - 1)/2
b) 4B = 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101
=> 4B - B = (4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101) - (1 + 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 )
=> 3B = 4^101 - 1 => B = ( 4^101 - 1)/2
c) xem lại đề ý c xem quy luật như thế nào nhé.
d) 3D = 3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151
=> 3D - D = (3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151) - (3 ^100 + 3 ^ 101 + 3 ^ 102 + .... + 3 ^ 150)
=> 2D = 3^ 151 - 3^100 => D = ( 3^ 151 - 3^100)/2

a) Có A=\(1+3+3^2+3^3+....+3^{100}\)

\(\Rightarrow\)3A =\(3\left(1+3+3^2+3^3+...+3^{100}\right)\)=\(3+3^2+3^3+3^4+...+3^{101}\)

\(\Rightarrow2A=3+3^2+3^3+....+3^{101}-1-3-3^2-3^3-....-3^{100}=3^{101}-1\)\(\Rightarrow A=\dfrac{3^{101}-1}{2}\)

Bài b/c/d : bn cứ lm tương tự.

a) 2³ = 8; 2⁴ = 16; 2⁵ = 32; 2⁶ = 64; 2⁷ = 128; 2⁸ = 256; 2⁹ = 512; 2¹⁰ = 1024

b) 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243

c) 4² = 16; 4³ = 64; 4⁴ = 256

d) 5² = 25; 5³ = 125; 5⁴ = 625

c) 6² = 36; 6³ = 216; 6⁴ = 1296

a) 2³ = 8; 2⁴ = 16; 2⁵ = 32; 2⁶ = 64; 2⁷ = 128; 2⁸ = 256; 2⁹ = 512; 2¹⁰ = 1024

b) 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243

c) 4² = 16; 4³ = 64; 4⁴ = 256

d) 5² = 25; 5³ = 125; 5⁴ = 625

e) 6² = 36; 6³ = 216; 6⁴ = 1296

HT

A = 4 + 4⁴ + 4⁷  + ... + 4³¹ 

4³A = 4³.(4 + 4⁴ + 4⁷ + ... + 4³¹) 

64A = 4⁴ + 4⁷ + 4¹⁰ + ... + 4³⁴ 

64A - A = (4⁴ + 4⁷ + ... + 4³⁴) - (4 + 4⁴ + ... + 4³¹) 

63A = 4³⁴ - 4 

=> A = \(\frac{4^{34}-4}{63}\)

a=2mu 101 - 2

b= 3 mu 2010 - 1

c=5mu 1999-1

d=4 mu n . 4 -4

a=2+2²+...+2¹⁰⁰

2a=2²+2³+2⁴+...+2¹⁰¹

a=2a-a=a

=> a= 2²+2³+2⁴+..+2¹⁰¹ -(2+2^2+...+2^100)

=>a= 2^101 -2 

\(A=4+4^2+...+4^{99}\)

\(\Rightarrow4A=4^2+3^3+...+4^{99}+4^{100}\)

\(\Rightarrow4A-A=4^{100}-4\)

\(\Rightarrow3A=4^{100}-4\Rightarrow A=\frac{4^{100}-4}{3}\)

\(B=5+5^2+...+5^{10}\)

\(5B=5^2+5^3+...+5^{10}+5^{11}\)

\(5B-B=4B=5^{11}-5\Rightarrow B=\frac{5^{11}-5}{4}\)

C đang 6 mũ sao tự nhiên nhảy đâu ra 9 mũ?

Nếu nó là 6 mũ thì làm tương tự như 2 câu trên

Ai đó help me mai lộp rồi