Question

1. Chứng minh: 

a) (2¹ + 2² + 2³+ ..................+ 2²⁰¹⁵+ 2²⁰¹⁶) CHIA HẾT 3 = ?

b) ( 10¹⁰⁰ + 2) CHIA HẾT 3 = ?

Answer 1

b) ( 10¹⁰⁰ + 2) : 3 

= (1000 + 2) : 3

= 1002 : 3

= 334

Answer 2

a)A= (2¹ + 2² + 2³+ ..................+ 2²⁰¹⁵+ 2²⁰¹⁶) : 3

2A=2(2¹+2²+2³+...+2²⁰¹⁵+2²⁰¹⁶):3

2A=(2²+2³+2⁴+...+2²⁰¹⁶+2²⁰¹⁷):3

2A-A=[(2²+2³+2⁴+...+2²⁰¹⁶+2²⁰¹⁷)-(2¹+2²+2³+...+2²⁰¹⁵+2²⁰¹⁶)]:3

A=(2²⁰¹⁷-2):3