Question

Cho A = 1 + 5 + 5² + 5³ + 5⁴ + ...+ 5²⁰¹⁷

B = 5²⁰¹⁸ - 1

So sánh 4A với B

Answer 1

Ta có:

A = 1 + 5 + 5² + 5³ + 5⁴ + ...+ 5²⁰¹⁷

A = \(\frac{5^{2017}-1}{5-1}\)

B = \(\frac{5^{2018}-1}{2-1}\)

=> \(4A=\frac{5^{2017}-1}{4}.4=5^{2017}-1< B=5^{2018}-1\)

Vậy 4A < B

Answer 2

Ta có: 5A=5(1+5+5²+....+5²⁰¹⁷)

          5A=5+5²+5³+....+5²⁰¹⁸

          5A-A=(5+5²+5³+...+5²⁰¹⁸)-(1+5+5²+....+5²⁰¹⁷)

          4A=5²⁰¹⁸-1

Vì 4A=5²⁰¹⁸-1. Mà 5²⁰¹⁸-1=5²⁰¹⁸-1

Suy ra:4A=B