Toán Lớp 6: Cho S = 5 + 5 mũ 2 + 5 mũ 3 + 5 mũ 4+ 5 mũ 5 + 5 mũ 6 +…+ 5 mũ 2012 CTR S chia hết cho 65
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Toán Lớp 6: Cho S = 5 + 5 mũ 2 + 5 mũ 3 + 5 mũ 4+ 5 mũ 5 + 5 mũ 6 +…+ 5 mũ 2012 CTR S chia hết cho 65
Comments ( 2 )
S=(5+5^2+5^3+5^4)+(5^5+5^6+5^7+5^8)+…+(5^2009+5^2010+5^2011+5^2012)
S=(5+5^2+5^3+5^4)+5^5(5+5^2+5^3+5^4)+…+5^2009(5+5^2+5^3+5^4)
Ta có:
5+5^2+5^3+5^4
=(5+5^3)+(5^2+5^4)
=(5+5^3)+5(5+5^3)
=(5+125)+5(5+125)
=130+5.130
=2.65+5.2.65
=2.65+10.65
=65(2+10) vdots65
=>(5+5^2+5^3+5^4)vdots65
Vì :
(5+5^2+5^3+5^4)vdots65
=>5^5(5+5^2+5^3+5^4)vdots65
…………………
5^2009(5+5^2+5^3+5^4)vdots65
=>S vdots 65