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det. ultima cifra a numarului n unde n =1+1+2+2^2+2^3+..........2^2004

Răspuns :

[tex]S=1+1+2+2^2+2^3+...+2^{2004}\\ S-1=1+2+2^2+2^3+...+2^{2004}|*2\\ 2S-2=2+2^2+2^3+...+2^{2005}\\ 2S-2-S+1=2+2^2+...+2^{2005}-1-2-2^2-2^3-...-2^{2004}\\ S-1=2^{2005}-1\\ S=2^{2005}\\ Si\ sper\ ca\ sti\ sa\ faci\ si\ singur\ de \aici.[/tex]