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cine rezolva problemele de la titularizare 2007?
subiectele se afla pe subiecte2007.edu.ro
sub.1 d),f),g)
sub.2 g)
sub.3 d),e),g)
daca se poate si metodica...
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profesor
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EU AM INTAMPINAT GREUTATI LA I PCT.C,F,G
IIE,G
IIIG
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1c)
P(n): 1+1/2+1/3+...+1/2^n>=n/2+1,n>=1
verificare
n=1
1+1/2>=1+1/2 adev
P(n+1): 1+1/2+1/3+...+1/2^n+1/2^n+1+...1/2^n+2^n>=(n+1)/2+1
1/2^n+1+...+1/2*2^n>=1/2*2^n+...+1/2*2^n=1/2
1+1/2+1/3+...+1/2^n+1/2^n+1+...1/2^n+2^n>=n/2+1+1/2=(n+1)/2+1
deci
P(n) adevarat
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