Question

Cho A=1+3¹+3²+.........+3⁹⁹

a/ Chung minh A chia het cho 4

b/CM A chia het cho 40

Answer 1

A = 1 + 3^1 + 3^2 + ... + 3^99

3A = 3 + 3^2+ 3^3 + ... + 3^100

3A = ( 3 + 3^2 ) + ( 3^3 + 3^4 ) + ... + ( 3^99 + 3^100 )

3A = 3 ( 1 + 3 ) + 3^3 ( 1 + 3 )  + ... + 3^99 ( 1 + 3 )

3A = 3 . 4 + 3^3 . 4 + ... + 3^99 . 4

3A = 4 . ( 3 + 3^3 + 3^99 ) \(⋮\)4

Answer 2

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