5: 2^103-2^102=2^102(2-1)=2^102
4*3^100+5*3^100=3^100*9=3^102
=> 2^103-2^102<4*3^100+5*3^100
6: 75*5^2003=5^2005*3=15*5^2004
2*125^668+20*5^2003
=2*5^2004+5^2004*4
=6*5^2004
=>75*5^2003>2*125^668+20*5^2003
7: A=1+2+2^2+...+2^2005
=>2A=2+2^2+...+2^2006
=>A=2^2006-1<2^2006+2^2004
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