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aratati ca n e patrat perfect(prin factor comun) daca n=100+2×(1+2+3+....99)

Răspuns :

19999991
[tex]n = 100 + 2 \times (1 + 2 + 3 + ... + 99)[/tex]

[tex]n = 100 + 2 \times \frac{99 (99 + 1)}{2} [/tex]

[tex]n = 100 + 99(99 + 1)[/tex]

[tex]n = 100 + 99 \times 100[/tex]

[tex]n = 100(1 + 99)[/tex]

[tex]n = 100 \times 100[/tex]

[tex]n = 10000[/tex]

[tex]n = {100}^{2} = > p.p[/tex]

n=100+2×(1+2+3+...99)

n=100+2×(99×100):2

n=100+99×100

n=100 (1+99)

n=100×100

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