Question

Suma primelor 100 zecimale ale numărului
37
este egală cu:
33
A. 100
B. 150
C. 200
D. 300
cu demonstratie va rog!!​

Answer 1

 

$\displaystyle\bf\\\frac{^{3)}37}{33}=~~~(Amplificam~cu~3~pentru~a~obtine~99~la~numitor.)\\\\=\frac{111}{99}=~~(Scoatem~intregii)\\\\=1\frac{12}{99}=1,\!(12)\\\\\textbf{Calculam suma primelor 100 de zecimale.}\\\\100:2=50\\\\\implies~avem~50~de~grupe~de~forma~(12)\\ Suma~cifrelor~dintr-o~grupa~este:\\\\1+2=3\\\\Suma~cifrelor~din~50~de~grupe~este:\\\\50(1+2)=50\times3=\boxed{\bf150}\\\\Raspuns~corect~B.$