Question

Aratati ca nr n=100+2×(1+2+3+4+...+99) este patrat perfect urgennnttt

Answer 1

$n = 10 0+ 2 \times (1 + 2 + 3 + 4 + ... + 99)$

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

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

$n = 100 + 99 \times 100$

$n = 100(1 + 99)$

$n = 100 \times 100$

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

Answer 2

n = 100 + 2 × ( 1 + 2 + 3 + 4 + ...... + 99 )

n = 100 + 2 × 99 × ( 1 + 99 ) : 2

n = 100 + 99 × 100

n = 100 × ( 1 + 99 ) → am dat factor comun pe 100

n = 100 × 100

n = 100² → patrat perfect