\(A=\frac{1}{5}+\frac{1}{5^3}+\frac{1}{5^5}+...+\frac{1}{5^{101}}\)

\(\frac{1}{5^2}A=\frac{1}{5^3}+\frac{1}{5^5}+\frac{1}{5^7}+...+\frac{1}{5^{103}}\)

\(\left(1-\frac{1}{5^2}\right)A=\left(\frac{1}{5}+\frac{1}{5^3}+\frac{1}{5^5}+...+\frac{1}{5^{101}}\right)-\left(\frac{1}{5^3}+\frac{1}{5^5}+\frac{1}{5^7}+...+\frac{1}{5^{103}}\right)\)

\(\frac{24}{25}A=\frac{1}{5}-\frac{1}{5^{103}}\)

\(A=\left(1-\frac{1}{5^{102}}\right).\frac{5}{24}\)

Suy ra \(\left(\frac{1}{5}+\frac{1}{5^3}+\frac{1}{5^5}+...+\frac{1}{5^{101}}\right)\div\left(1-\frac{1}{5^{102}}\right)=\frac{5}{24}\).

giúp mình với tối nay mình cần

27⁵-9⁷+3¹³=3¹⁵-3¹⁴+3¹³=3¹³(9-3+1)=3¹³.7 chia hết cho 7  suy ra 27⁵ - 9⁷ + 3¹³ chia hết cho 7

Ta có: 27⁵ - 9⁷ + 3¹³

= (3³)⁵ - (3²)⁷ + 3¹³

= 3¹⁵ - 3¹⁴ + 3¹³

= 3¹³ (3² - 3 + 1)

= 3¹³ . 7

Vì 3¹³ . 7 chia hết cho 7 nên 27⁵ - 9⁷ + 3¹³ chia hết cho 7

a. 5x.(12x + 7) - 3x(20x - 5) = - 100

↔ 60x2 + 35x - 60x2 + 15x = - 100

↔ 50x = - 100

→ x = - 2

b. 0,6x(x - 0,5) - 0,3x(2x + 1,3) = 0,138

↔ 0,6x2 - 0,3x - 0,6x2 - 0,39x = 0,138

↔ - 0,6x = 0,138

↔ x = 0,138 : (- 0,6)

↔ x = - 0,2

Bài 4. Tìm x biết:

a) 5x(12x + 7) – 3x(20x – 5) = - 100

\(\Leftrightarrow60x^2+35x-60x^2+15x=-100\)

\(\Leftrightarrow50x=-100\)

\(\Leftrightarrow x=-2\)

b) 0,6x(x – 0,5) – 0,3x(2x + 1,3) = 0,138

\(\Leftrightarrow0,6x^2-0,3x-0,6x^2-0,39x=0,138\)

\(\Leftrightarrow-0,69x=0,138\)

\(\Leftrightarrow x=-0,2\)

c) 6x(5x + 3) + 3x(1 – 10x) = 7

\(\Leftrightarrow30x^2+18x+3x-30x^2=7\)

\(\Leftrightarrow21x=7\)

\(\Leftrightarrow x=\frac{1}{3}\)

a)

x(2x + 1) - x²(x + 2) + (x³ - x + 3)

\(=2x^2+x-x^3-2x^2+x^3-x+3\)

\(=\left(x^3-x^3\right)+\left(2x^2-2x^2\right)+\left(x-x\right)+3\)

\(=3\)\(\left(ĐPCM\right)\)

b)

x(3x² - x + 5) - (2x³ +3x - 16) - x(x² - x + 2)

\(=3x^3-x^2+5x-2x^3-3x+16-x^3+x^2-2x\)

\(=\left(3x^3-2x^3-x^3\right)-\left(x^2-x^2\right)+\left(5x-3x-2x\right)+16\)

\(=16\left(ĐPCM\right)\)

d) là 3 phần -4 nha, 2 người đầu sẽ k

Hình đây nha,mk thấy đề sai nên k làm chỗ tổng 3 gióc í