Question

1. Tìm x :

3x−2.4=324

2x<20

(52x.5x+1)÷5=125

2. Tính :

C=1+5²+5⁴+5⁶+.........+5²⁰¹⁶

A=1+3+3²+......+3²⁰¹⁶

B=1+6+6²+................+6²⁰⁰

 

Answer 1

mk học dạng này rồi nên bạn yên tâm là đúng nhé

2.

A = 1+3+3² +....+3²⁰¹⁶

3A= (1+3+3²+.....+3²⁰¹⁶) . 3

3A= 3+3² + 3³+.....+ 3²⁰¹⁷

3A-A = (3+3² + 3³+.....+ 3²⁰¹⁷) - (1+3+3² +....+3²⁰¹⁶)

2A    = 3²⁰¹⁷   - 1

A= (3²⁰¹⁷ - 1) : 2

Answer 2

\(C=1+5^2+5^4+5^6+...+5^{2016}\)

\(\Rightarrow5^2C=5^2+5^4+5^6+...+5^{2018}\)

\(\Rightarrow25C-C=\left(5^2+5^4+5^6+...+5^{2018}\right)-\left(1+5^2+5^4+...+5^{2016}\right)\)

\(\Rightarrow24C=5^{2018}-1\)

\(\Rightarrow C=\frac{5^{2018}-1}{24}\)

Answer 3

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

\(\Rightarrow3A=3+3^2+3^3+...+3^{2017}\)

\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{2017}\right)-\left(1+3+3^2+...+3^{2016}\right)\)

\(\Rightarrow2A=3^{2017}-1\)

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

 

Answer 4

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

\(\Rightarrow6B=6+6^2+6^3+...+6^{201}\)

\(\Rightarrow6B-B=\left(6+6^2+6^3+...+6^{201}\right)-\left(1+6+6^2+...+6^{200}\right)\)

\(\Rightarrow5B=6^{201}-1\)

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