Question

Giúp mk vs:

Rút gọn biểu thức :

a,A=\(\frac{6^3+3\cdot6^2+3^3}{-13}\)

b, A=1+5+5²+5³⁺5^4+...+5⁴⁹⁺5⁵⁰

c, A= 2^100-2⁹⁹+2^98-2^97+...+2²-2

 

 

Answer 1

a) 

\(A=\frac{6^3+3.6^3+3^3}{-13}=\frac{3^3.2^3+3^3.2^2+3^3}{-13}=\frac{3^3\left(8+4+1\right)}{-13}=\frac{27.13}{-13}=-27\)

b)

A=1+5+5²+5³+...+5⁵⁰

5A=5+5²+5³+...5⁵¹

5A-A=(5+5²+5³+...+5⁵¹)-(1+5+5²+...+5⁵⁰)

4A=5⁵¹-1

A=\(\frac{5^{51}-1}{4}\)

c)

A=2¹⁰⁰-2⁹⁹+2⁹⁸-...+2²-2

2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-...+2³-2²

2A+A=(2¹⁰¹-2¹⁰⁰+...+2³-2²)+(2¹⁰⁰-2⁹⁹+...+2²-2)

3A=2¹⁰¹-2

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

 

Answer 2

b.

\(A=1+5+5^2+5^3+...+5^{49}+5^{50}\)

\(5A=5+5^2+5^3+...+5^{50}+5^{51}\)

\(5A-A=\left(5+5^2+5^3+...+5^{50}+5^{51}\right)-\left(1+5+5^2+..+5^{50}\right)\)

\(4A=5^{51}-1\)

\(A=\frac{5^{51}-1}{4}\)

Answer 3

a) 

\(A=\frac{6^3+3.6^2+3^3}{13}=\frac{2^3.3^3+3.3^2.2^2+3^3}{13}=\frac{3^3\left(2^3+2^2+1\right)}{13}=\frac{27.13}{13}=27\)

b)

A=1+5+5²+5³+...+5⁵⁰

5A=5+5²+5³+...5⁵¹

5A-A=(5+5²+5³+...+5⁵¹)-(1+5+5²+...+5⁵⁰)

4A=5⁵¹-1

A=\(\frac{5^{51}-1}{4}\)

c)

A=2¹⁰⁰-2⁹⁹+2⁹⁸-...+2²-2

2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-...+2³-2²

2A+A=(2¹⁰¹-2¹⁰⁰+...+2³-2²)+(2¹⁰⁰-2⁹⁹+...+2²-2)

3A=2¹⁰¹-2

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

Answer 4

c.

\(A=2^{100}-2^{99}+2^{98}-....-2^3+2^2-2\)

\(2A=2^{201}-2^{100}+2^{99}-...-2^4+2^3-2^2\)

\(2A+A=\left(2^{101}-2^{100}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+..+2^2-2\right)\) \(3A=2^{201}-2\)

\(A=\frac{2^{201}-2}{3}\)

Answer 5

a.

\(A=\frac{6^3+3.6^2+3^3}{-13}=\frac{216+3.36+27}{-13}=\frac{351}{-13}=-27\)