Question

Ajutor. Va rog! Cum îl pot afla pe x? Îmi puteți explica? ​

Answer 1

Explicație pas cu pas:

Answer 2

$x=\frac{5}{1}+\frac{9}{2}+\frac{13}{3}+...+\frac{8061}{2015}-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})$

$x=\frac{4\cdot 1 +1}{1}+\frac{4\cdot 2+1}{2}+\frac{4\cdot 3+1}{3}+...+\frac{4\cdot 2015+1}{2015}-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})$

$x=(\frac{4\cdot 1}{1}+\frac{1}{1})+(\frac{4\cdot 2}{2}+\frac{1}{2})+(\frac{4\cdot 3}{3}+\frac{1}{3})+...+(\frac{4\cdot 2015}{2015}+\frac{1}{2015})-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})$

$x=(4+1)+(4+\frac{1}{2})+(4+\frac{1}{3})+...+(4+\frac{1}{2015})-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})\\ \\ x=4\cdot 2015 + (1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015})\\ \\ x=4\cdot 2015\\ \\ (\frac{x}{4}-2014)^{2015}=\\ \\=(\frac{4\cdot 2015}{4}-2014)^{2015}=\\ \\ =(2015-2014)^{2015}=\\ \\ =1^{2015}=\\ \\=1$