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Daca x apartine N si 1+3+5+....+(2x-1)=100. atunci x= ?


Răspuns :

[tex]\displaystyle 1+3+5+...+(2x-1)=100 \\ \\ 1+2+3+4+5+...+(2x-1)-(2+4+6+...+2x)=100 \\ \\ \frac{(2x-1)(2x-1+1)}{2} -2(1+2+3+4+...+x)=100 [/tex]

[tex]\displaystyle \frac{(2x-1) \cdot \not2x}{\not2} -2 \cdot \frac{x(x+1)}{2} =100 \\ \\ (2x-1) \cdot x-\not2 \cdot \frac{x^2+x}{\not2} =100 \\ \\ 2x^2-x-x^2+x=100 \\ \\ x^2=100 \\ \\ x= \sqrt{100} \\ \\ x=10[/tex]

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