Question

Tính tổng :

Q= 1+3 mũ 3 + 3 mũ 6 + 3 mũ 9 +.....+3 mũ 99

Answer 1

     Q =  1 + 3³ + 3⁶ + 3⁹ + ... + 3⁹⁹

3³Q =   3³ + 3⁶ + 3⁹ + 3¹²+ ...+ 3¹⁰²

27Q - Q = 3³ + 3⁶ + 3⁹ + 3¹² +... + 3¹⁰² - (1 + 3³ + 3⁶ + 3⁹ + ... + 3⁹⁹)

26Q = 3³ + 3⁶ + 3⁹ + 3¹² + ... + 3¹⁰² - 1 - 3³ - 3⁶ - 3⁹ - ...- 3⁹⁹

26Q = (3¹⁰² - 1) + (3³ - 3³) + (3⁶ - 3⁶) + ... + (3⁹⁹ - 3⁹⁹)

26Q = 3¹⁰² - 1 + 0  + 0 + 0 + ... + 0

26Q = 3¹⁰² - 1

Q = \(\dfrac{3^{102}-1}{26}\)