Question

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

Answer 1

$n = 100 + 2 \times (1 + 2 + 3 + ... + 99)$

$n = 100 + 2 \times \frac{99 (99 + 1)}{2}$

$n = 100 + 99(99 + 1)$

$n = 100 + 99 \times 100$

$n = 100(1 + 99)$

$n = 100 \times 100$

$n = 10000$

$n = {100}^{2} = > p.p$

Answer 2

n=100+2×(1+2+3+...99)

n=100+2×(99×100):2

n=100+99×100

n=100 (1+99)

n=100×100