Question

Calculand S=2•2 la 2 +3•2 la 3 +4•2 la 4 +...+10•2 la 10 , obtinem:
A) 9•2 la 11 B) 10•2 la 11 C) 11•2 la 10 D) 11•2 la 11 E) 10•2 la 12
Va rog repedee !!!

Answer 1

S=$2* 2^{2} +3* 2^{3} +4* 2^{4} +5* 2^{5} +6* 2^{6} +7* 2^{7} +8* 2^{8}+9* 2^{9} +10*$$2^{10} = 2^{3} +3* 2^{3} + 2^{6} +5* 2^{5} +3* 2^{7}+7* 2^{7} + 2^{11} +9* 2^{9} +5* 2^{11}$=$4* 2^{3} + 2^{6} +5* 2^{5} +10* 2^{7} +$$6*2^{11} +9* 2^{9}= [tex] 2^{5} + 2^{6} +5* 2^{5} +5* 2^{8} +9* 2^{9}$$+3* 2^{12}=$$6* 2^{5} + 2^{6} +5* 2^{8} +9* 2^{9} +3* 2^{2012} =3* 2^{6} + 2^{6} +5* 2^{8} +9* 2^{9} +$$3* 2^{12} =$$4* 2^{6} +5* 2^{8} +9* 2^{9} +3* 2^{12} = 2^{8} +5* 2^{8} +9* 2^{9} +3* 2^{12} =6*$$2^{8} +9* 2^{9} +3* 2^{12} =3* 2^{9} +9* 2^{9} +3* 2^{12} =6* 2^{9} +3* 2^{12} =3*$$2^{11} +3* 2^{12} =3* 2^{11} *(1+2)=3*3* 2^{11} =9* 2^{11}$
raspuns corect A