Question

S= 1+5+9+13+........+2013 +2017 tính tổng

cho A= 1+3+3^2+3^3+....+3^2016 và B = 3^2017 tinh B-A

 

Answer 1

a) Ta có:

S = 1 + 5 + 9 + 13 + ... + 2013 + 2017

S = (2017 + 1)[(2017 - 1) : 4 + 1] : 2

S = 2018.505 : 2

S = 1019090 ÷ 2

S = 509545

b) Ta có:

A = 1 + 3 + 3² + 3³ + ... + 3²⁰¹⁶

3A = 3 + 3² + 3³ + 3⁴ + ... + 3²⁰¹⁷

3A - A = (3 + 3² + 3³ + 3⁴ + ... + 3²⁰¹⁷) - (1 + 3 + 3² + 3³ + ... + 3²⁰¹⁶)

2A = 3²⁰¹⁷ - 1

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

=> B - A = 3²⁰¹⁷ - \(\frac{3^{2017}-1}{2}\)

=> B - A = 3²⁰¹⁷ - \(\frac{3^{2017}}{2}-\frac{1}{2}\)

=> B - A = \(\frac{3^{2017}}{2}-0,5\)