Question

Cho A = 3^1+3^2+3^3+.....3^2012

CMR:A chia hết cho 13

Answer 1

A = 3¹ + 3² + 3³ + ..... + 3²⁰¹²

A = ( 3¹ + 3² + 3³)  + ......... + ( 3²⁰¹⁰ + 3²⁰¹¹ + 3²⁰¹²)

A = 1. ( 3¹ + 3² + 3³) + ........ + 3²⁰¹⁰. ( 3¹ + 3² + 3³) 

A = 1 . 39 + ....... + 3²⁰¹⁰ . 39

A = 39 . ( 1 + ...... + 3²⁰¹⁰) \(⋮13\rightarrowĐPCM\)

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