Question

demonstrati ca n=105+2(1+2+3+4+......+104) este patrat perfect

Answer 1

n = 105 + 2 ( 1 + 2 + 3 + 4 + .......+ 104 )

n = 105 + 2 × ( 104 × 105 ) / 2 → aplic formla sumei lui Gauss

1 + 2 + 3 + ......+ 104 = 104 ( termeni ) x ( 1 + 104 ) / 2 = 104 × 105 / 2

→ 2 / 2 = 1

n = 105 + 104 × 105

n = 105 ( 1 + 104 )

n = 105 × 105

n = 105²→ patrat perfect