Question

Se considera sirul 1 22 333 4444 55555 determinati al 2012 lea termen al sirului
Dau coronita

Answer 1

1, 22, 333, 4444, 55555

Se mai poate scrie: 

$1\cdot 10^0, 2\cdot10^1 + 2\cdot 10^0, 3\cdot 10^2+3\cdot 10^1+3\cdot 10^0, 4\cdot 10^3+...+4\cdot 10^0, \\ \\ 5\cdot10^4+...+5\cdot 10^0 \\ \\ \\ Scris mai exact: 1\cdot 10^0, 2\cdot(10^1+10^0), 3\cdot(10^2+10^1+10^0), \\ \\ 4\cdot(10^3+...+10^0), 5\cdot(10^4+...+10^0) \\ \\ \\ Deci, al 2012-lea termen este: 2012\cdot(10^{2011}+ 10^{2010}+...+10^0) = \\ \\ =2012\cdot(10^{0}+ 10^{1}+...+10^{2011}) = 2012\cdot \dfrac{10^{2012}-1}9}=$

= (numarul atasat din imagine)