Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha

1, 7A = 7+7^2+7^3+....+7^2008

6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1

=> A = (7^2008-1)/6

Tk mk nha

\(A=1+7+7^2+7^3+...+7^{2007}\)

\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)

\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)

\(\Rightarrow6A=7^{2008}-1\)

\(\Rightarrow A=\frac{7^{2008}-1}{6}\)

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

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

3b=4^101-1

b=(4^101-1):3

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.

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cho mi sửa lại:

\(a) A = 1^2+2^3+3^4+...+2014^{2015} b) B = 101^2+102^2+...+199^2+200^2 c) C = 1^3+2^4+3^5+4^6+...+99^{101}+100^{102}\)

dấu 8 là nhân còn dấu ^ là mũ ạ

troi,zậy mà khó

a) 2 x 2 = 4              3 x 3 = 9

2 x 4 = 8              3 x 5 = 15

2 x 6 = 12              3 x 7 = 21

2 x 8 = 16              3 x 9 = 27

4 x 4 = 16              5 x 5 = 25

4 x 2 = 8              5 x 7 = 35

4 x 6 = 24              5 x 9 = 45

4 x 8 = 32              5 x 3 = 15

b) 200 x 4 = 800              300 x 2 = 600

200 x 2 = 400             300 x 3 = 900

400 x 2 = 800             500 x 1 = 500

100 x 4 = 400             100 x 3 = 300

Trả lời 1 câu thôi nhé em 100 nhân 4 bằng 400 nhá em

a) 2 x 2 =4 ......              3 x 3 = ..9....

2 x 4 = ....8..              3 x 5 = ...15...

2 x 6 = ....12..              3 x 7 = .21.....

2 x 8 = ..16....              3 x 9 = ..27....

4 x 4 = ...16...              5 x 5 = ...25...

4 x 2 = ...8...              5 x 7 = ..35....

4 x 6 = .....24.              5 x 9 = .45.....

4 x 8 = ..32....              5 x 3 = .15.....

b) 200 x 4 = 800......              300 x 2 =600 ......

200 x 2 = ..400....             300 x 3 = 900......

400 x 2 = .....800.             500 x 1 = ..500....

100 x 4 = ....400..             100 x 3 = .300.....

Đăt A = \(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+......+\frac{1}{7^{100}}\)

\(\Rightarrow7A=1+\frac{1}{7}+\frac{1}{7^2}+.....+\frac{1}{7^{100}}\)

\(\Rightarrow7A-A=1-\frac{1}{7^{100}}\)

\(\Rightarrow6A=1-\frac{1}{7^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{7^{100}}}{6}\)

a)

   \(2A=2+2^2+2^3+...+2^{101}\)

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

\(A=2^{101}-1\)

b)

  Tách ra thành 2 tổng :\(D=3+3^3+...+3^{99}\) và \(E=3^2+3^4+...+3^{100}\)

\(3^2D=3^3+3^5+...+3^{101}\)

\(9D-D=\left(3^3+3^5+...+3^{101}\right)-\left(3+3^3+...+3^{99}\right)\)

\(8D=3^{101}-3\Leftrightarrow D=\frac{3^{101}-3}{8}\)

Tương tự \(E=\frac{3^{102}-3^2}{8}\)

Ta có \(D-E=B\)

Do đó \(\frac{3^{101}-3-3^{102}+3^2}{8}\)

Tương tự phần a, b tính được \(C=\frac{5^{202}-1}{24}\)

c,\(C=1+5^2+5^4+5^6+...+5^{200}\)

\(\Rightarrow25C=5^2+5^4+5^6+5^8+...+5^{202}\)

\(\Rightarrow25C-C=24C=\left(5^2+5^4+...+5^{202}\right)-\left(1+5^2+...+5^{200}\right)\)

\(=5^{202}-1\)

\(\Rightarrow C=\frac{5^{202}-1}{24}\)