Question

Cho B= 3 mũ 1+ 3 mũ 2+ 3 mũ 3+ 3 mũ 4 + 3 mũ 5+...+3 mũ 100

Chứng tỏ B chia hết cho 2

 

Answer 1

\(\Rightarrow3B=3^2+3^3+3^4+...+3^{101}\\ \Rightarrow3B-B=3^2+3^3+...+3^{101}-3-3^2-3^3-...-3^{100}\\ \Rightarrow2B=3^{101}-3\\ \Rightarrow B=\dfrac{3^{101}-3}{2}\)

Answer 2

B = 3¹ + 3² + 3³ + .... + 3⁹⁹ + 3¹⁰⁰

3B = 3(3¹ + 3² + 3³ + ..... + 3⁹⁹ + 3¹⁰⁰)

3B = 3² + 3³ + 3⁴ +...... + 3¹⁰⁰ + 3¹⁰¹

3B - B = 2B = (3² + 3³ + 3⁴ + .... + 3¹⁰⁰ + 3¹⁰¹) - ( 3¹ + 3² + 3³ + .... + 3¹⁰⁰)

2B = (3² - 3²) + (3³ - 3³) +.....+ ( 3¹⁰⁰ - 3¹⁰⁰) + ( 3¹⁰¹ - 1)

2B = 0 + 0 + 0 + ..... +0 + 3¹⁰¹ - 1

2B = 3¹⁰¹ - 1

B = (3¹⁰¹ - 1)  : 2