Question

rút gọn biển thức sau: A=1+3+3²⁺3³+...+3¹⁰⁰

^{GIÚP MIK VS MNG ƯI CẺM ƠN MN TRC}

Answer 1

A = 1 + 3 + 3² + 3³ +.... +3¹⁰⁰

3A = 3(1 + 3 + 3² + 3³ +....+3¹⁰⁰)

3A = 3 + 3² + 3³ + 3⁴ +....+3¹⁰¹

3A - A = 2A = (3 + 3² + 3³ + 3⁴ +.... + 3¹⁰¹) - (1 + 3 + 3² + .... + 3¹⁰⁰)

2A = ( 3 - 3 ) + ( 3² - 3²) +.....+ (3¹⁰⁰ - 3¹⁰⁰) + (3¹⁰¹ - 1)

2A = 0 + 0 +....+ 0 + 3¹⁰¹ - 1

2A = 3¹⁰¹ - 1

A = (3¹⁰¹ - 1) : 2

Answer 2

\(\Rightarrow3A=3+3^2+3^3+...+3^{101}\)

\(\Rightarrow3A-A=3+3^2+3^3+...+3^{101}-1-3-3^2-...-3^{100}\)

\(\Rightarrow2A=3^{101}-1\)

\(\Rightarrow A=\dfrac{3^{101}-1}{2}\)