Question

Te rog ajuta ma si pe mine si te voi rasplati cu o coroana!
a=(1+2+.....+1994):1995; b=(2^17x4^8)^1995:8^665. Calculati: 2(a+b)-1

Answer 1

a = (1+2+...+1994) : 1995
= 1994 * 1995 : 2 : 1995
= 1994 : 2 * 1995 : 1995
= 1994 : 2 = 997

$b=(2^{17}:4^8)^{1995}:8^{665} \\ \\ =[2^{17}:(2^2)^8]^{1995}:(2^3)^{665} \\ \\ =(2^{17}:2^{16})^{1995}:2^{1995} \\ \\ =2^{1995}:2^{1995} \\ \\ =1$

2(a+b)-1 = 2*998-1 = 1995