Câu a:

1/3x = - 5/6

x = -5/6 : 1/3

x = -5/6 x 3

x = - 5/2

Vậy x = - 5/2

Câu b:

x : - 3/2 = - 4/5

x = - (4/5) x (-3/2)

x = 6/5

Vậy x = 6/5

Câu c:

x + 5/2 = -1 1/4

x + 5/2 = - 5/4

x = - 5/4 - 5/2

x = - 5/4 - 10/4

x = - 15/4

Vậy x = - 15/4

Câu d:

6/7 - x = - 1/14

x = 6/7 + 1/14

x = 12/14 + 1/14

x = 13/14

Vậy x = 13/14

\(A=1+3+3^2+...+3^{2016}\)

\(3A=3.\left(1+3+3^2+...+3^{2016}\right)\)

\(3A=3+3^2+3^3+...+3^{2017}\)

\(3A-A=\left(3+3^2+3^3+...+3^{2017}\right)-\left(1+3+3^2+...+3^{2016}\right)\)

\(2A=3^{2017}-1\)

\(A=\left(3^{2017}-1\right):2\)

\(B=1+6+6^2+...+6^{200}\)

\(6B=6.\left(1+6+6^2+...+6^{200}\right)\)

\(6B=6+6^2+6^3+...+6^{201}\)

\(6B-B=\left(6+6^2+6^3+...+3^{201}\right)-\left(1+6+6^2+...+6^{200}\right)\)

\(5B=6^{201}-1\)

\(B=\left(6^{201}-1\right):5\)

\(3^{x-2}.4=324\)

\(3^{x-2}=324:4\)

\(3^{x-2}=81\)

\(3^{x-2}=3^4\)

\(x-2=4\)

\(x=4+2\)

\(x=6\)

\(2x< 20\)

\(\Rightarrow x=\left\{0;1;2;3;4;5;6;7;8;9\right\}\)

\(\frac{x}{5}=\frac23\)

\(x\) = \(\frac23\times5\)

\(x=\frac{10}{3}\)

Vậy \(x=\frac{10}{3}\)

\(\frac{x}{3}-\frac12=\frac15\)

\(\frac{x}{3}\) = \(\frac15\) + \(\frac12\)

\(\frac{x}{3}\) = \(\frac{2}{10}+\frac{5}{10}\)

\(\frac{x}{3}=\frac{7}{10}\)

\(x=\frac{7}{10}\times3\)

\(x=\frac{21}{10}\)

Vậy \(x=\frac{21}{10}\)

\(\frac{x}{5}+\frac12=\frac{6}{10}\)

\(\frac{x}{5}=\frac{6}{10}-\frac12\)

\(\frac{x}{5}=\frac{6}{10}-\frac{5}{10}\)

\(\frac{x}{5}=\frac{1}{10}\)

\(x=\frac{1}{10}\times5\)

\(x=\frac12\)

Vậy \(x=\frac12\)

\(\frac{x+3}{15}\) = \(\frac13\)

\(x+3=\frac13\times15\)

\(x+3=5\)

\(x=5-3\)

\(x=2\)

Vậy \(x=2\)

Kết quả là 2870.

Giải nhanh bằng công thức tổng bình phương:

\(1^{2} + 2^{2} + \hdots + n^{2} = \frac{n \left(\right. n + 1 \left.\right) \left(\right. 2 n + 1 \left.\right)}{6}\)

Với \(n = 20\):

\(\frac{20 \cdot 21 \cdot 41}{6} = \frac{17220}{6} = 2870.\)

Ta có biểu thức:

\(1\times1+2\times2+3\times3+\ldots+20\times20=1^2+2^2+3^2+\ldots+20^2\)

Đây là tổng các số chính phương từ 1 đến 20.

Áp dụng công thức tổng bình phương:

\(1^2+2^2+3^2+\ldots+n^2=\frac{n \left(\right. n + 1 \left.\right) \left(\right. 2 n + 1 \left.\right)}{6}\)

Thay \(n = 20\):

\(\frac{20 \times 21 \times 41}{6} = \frac{17220}{6} = 2870\)

Cộng các tổng ở các mẫu số được:    \(S=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}.\) 

       \(\Leftrightarrow S=1+\frac{1}{2}\left(1-\frac{1}{3}\right)+\frac{1}{6}+\frac{1}{10}+\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{21}+\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{1}{36}.\) 

        Thực hiện các phép nhân một số với một hiệu ,được:

            \(S=1+\frac{1}{2}-\frac{1}{6}+\frac{1}{6}+\frac{1}{10}+\frac{1}{6}-\frac{1}{15}+\frac{1}{21}+\frac{1}{12}-\frac{1}{21}+\frac{1}{36}.\) 

         Giản ước, làm gọn được :   \(S=(1+\frac{1}{2})+(\frac{1}{10}+\frac{1}{6}-\frac{1}{15})+(\frac{1}{12}+\frac{1}{36}).\) 

            \(\Leftrightarrow S=\frac{3}{2}+\frac{1}{5}+\frac{1}{9}=\frac{135+18+10}{90}=\frac{163}{90}.\)

b,3².3ⁿ=3⁵

        3ⁿ=3⁵: 3²

         3ⁿ=3³

          n=3

\(a,2.16\le2^n< 4\)
\(\Rightarrow2^5\le2^n< 2^2\)
\(\Rightarrow n\in5,4,3\)
\(b,3^2.3^n=3^5\)
\(\Rightarrow3^n=3^5:3^2\)
\(\Rightarrow3^n=3^2\)
\(\Rightarrow n=2\)
\(c,\left(2^2:4\right):2^n=4\)
\(\Rightarrow1:2^n=4\)
\(\Rightarrow2^n=1:4=\frac{1}{4}\)
mà \(n\in N\)nên n ko có giá trị nào
\(d,\frac{1}{9}.3^4.3^n=3^7\)
\(\Rightarrow\left(\frac{1}{3}\right)^2.3^2.3^2.3^n=3^7\)
\(\Rightarrow3^2.3^n=3^7\)
\(\Rightarrow3^n=3^7:3^2\)
\(\Rightarrow3^n=3^5\)
\(\Rightarrow n=5\)

e,f làm tự làm tiếp nhé,mỏi tay wa

a) A = + + + .... +

2A = 2(+ + + .... +

A = (2¹ + 2² + 2³ + .... + 2²⁰¹¹) - (+ + + .... +

2²⁰¹¹ - 1

b) B = + + + .... +

3B = 3(+ + + .... +

2B = (3 + 3² + 3³ + .... + 3¹⁰¹) - (+ + + .... +

2B = 3¹⁰¹ - 1

B = (3¹⁰¹ - 1) : 2

c) C = + + + .... +

4C = 4(+ + + .... +

4C = + + 4⁴ .... +

3C = (+ + 4⁴ .... + + + + .... +

4^{n + 1} - 4) : 3

d) D = + + + .... +

5D = 5(+ + + .... +

+ + 5³ + .... +

(+ + 5³ + .... + (+ + + .... +

4D = (5²⁰⁰¹ - 1) : 4

a)\(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)

\(=\frac{45}{4}-\left(\frac{19}{7}+\frac{21}{4}\right)\)

\(=\frac{45}{4}-\left(\frac{76}{28}+\frac{147}{28}\right)\)

\(=\frac{45}{4}-\frac{223}{28}\)

\(=\frac{315}{28}-\frac{223}{28}\)

\(=\frac{23}{7}\)

b) \(\left(8\frac{5}{11}+3\frac{5}{8}\right)-3\frac{5}{11}\)

   \(=\left(\frac{93}{11}+\frac{29}{8}\right)-\frac{38}{11}\)

   \(=\left(\frac{744}{88}+\frac{319}{88}\right)-\frac{38}{11}\)

   \(=\frac{1063}{88}-\frac{38}{11}=\frac{1063}{88}-\frac{304}{88}\)

    \(=\frac{69}{8}\)

1a) \(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)

\(=11\frac{1}{4}-2\frac{5}{7}-5\frac{1}{4}\)

\(=11\frac{1}{4}-5\frac{1}{4}-2\frac{5}{7}\)

\(=6-2\frac{5}{7}=3\frac{2}{7}=\frac{23}{7}\)

2a) \(x\div8,25=\left(-2,2\right)\)

\(\Leftrightarrow x=-18,15\)

Câu a:

1/3x = - 5/6

x = -5/6 : 1/3

x = -5/6 x 3

x = - 5/2

Vậy x = - 5/2

Câu b:

x : - 3/2 = - 4/5

x = - (4/5) x (-3/2)

x = 6/5

Vậy x = 6/5

Câu c:

x + 5/2 = -1 1/4

x + 5/2 = - 5/4

x = - 5/4 - 5/2

x = - 5/4 - 10/4

x = - 15/4

Vậy x = - 15/4

Câu d:

6/7 - x = - 1/14

x = 6/7 + 1/14

x = 12/14 + 1/14

x = 13/14

Vậy x = 13/14

Câu a:

1/3x = - 5/6

x = -5/6 : 1/3

x = -5/6 x 3

x = - 5/2

Vậy x = - 5/2

Câu b:

x : - 3/2 = - 4/5

x = - (4/5) x (-3/2)

x = 6/5

Vậy x = 6/5

Câu c:

x + 5/2 = -1 1/4

x + 5/2 = - 5/4

x = - 5/4 - 5/2

x = - 5/4 - 10/4

x = - 15/4

Vậy x = - 15/4

Câu d:

6/7 - x = - 1/14

x = 6/7 + 1/14

x = 12/14 + 1/14

x = 13/14

Vậy x = 13/14