Arătați că 2+6+10+...+4026+2015 poate fi scris ca o sumă de două pătrate perfecte.

Răspunsul a fost dat de: USER7856
31 Agustus 2025 matematica 5 minute
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Clasă: Education Materie: matematica
Arătați că 2+6+10+...+4026+2015 poate fi scris ca o sumă de două pătrate perfecte.
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Cel mai bun răspuns
(183)
[tex]2+4+6+...+4026+2015=\\ 2(1+2+...+2013)+2015=\\ 2\cdot \frac{2013\cdot 2014}{2}+2015=2013\cdot2014+2015=\\ 2013\cdot2014+2014+1=2014(2013+1)+1=\\ 2014\cdot 2014+1=2014^2+1^2[/tex]
Răspunsul a fost dat în data 31 Agustus 2025
(173)
=2(1+2+3...+2013)+2015=
=2*2013*2014/2+2015=
=2013*2014+2015=
=2013*2014+2014+1=
=2014(2013+1)+1=
=2014*2014+1=
=2014^2+1^2=> pătrat perfect
Răspunsul a fost dat în data 31 Agustus 2025

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