Question

Cho S=3^0+3^2+3^4+3^6...........+3^2002

A.tính S

B.chứng minh:S chia hết cho 7

Answer 1

S=3^0+3^2+3^4+3^6+...+3^2002

=1+3^2+3^4+3^6+...+3^2002

9S=3^2+3^4+3^6+3^8+...+3^2004

9S-S=3^2+3^4+3^6+3^8+...+3^2004-1-3^2-3^4-3^6-...-3^2002

8S=3^2004-1

S=(3^2004-1):8

 

S=3^0+3^2+3^4+3^6+...+3^2002

=1+3^2+3^4+3^6+...+3^2002

=(1+3^2+3^4)+(3^6+3^8+3^10)+...+(3^1998+3^2000+3^2002)

=91+3^6(1+3^2+3^4)+...+3^1998(1+3^2+3^4)

91(1+3^6+...+3^1998)

ma 91 chia het cho 7

=> 91(1+3^6+...+3^1998) chia het cho 7

vay S chia het cho 7

Answer 2

chtt 

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