Question

Aflati x:
x(1 supra 1*3 +1 supra 3*5+ 1 supra 5*7+...+1 supra 61*63=2-64 supra 63
Urgent!

Answer 1

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Answer 2

[tex]\frac{x}{2}\cdot (\frac{2}{1\cdot 3}+\frac{2}{3\cdot 5}+...\frac{2}{61\cdot 63})=2-\frac{64}{63}\\ \frac{x}{2}\cdot(\frac{3-1}{1\cdot3}+\frac{5-3}{3\cdot5}+...\frac{63-61}{61\cdot 63})=2-1-\frac{1}{63}\\ \frac{x}{2}\cdot(\frac{3}{3}-\frac{1}{1\cdot3}+\frac{5}{3\cdot5}-\frac{3}{3\cdot5}+...\frac{63}{61\cdot63}-\frac{61}{61\cdot63})=1-\frac{1}{63}\\ \frac{x}{2}\cdot(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{61}-\frac{1}{63})=1-\frac{1}{63}\\ \frac{x}{2}(1-\frac{1}{63})=1-\frac{1}{63}\\ [/tex]
$x=2$