Question

S=2+4+6+8+10+...........+4034-2017 Demonstrati ca este patrat perfect

Answer 1

Răspuns:

S = 2 + 4 + .. + 4034 - 2017

= 2(1 + 2 + .. + 2017) - 2017

= 2×2017×2018 : 2 - 2017

= 2017×2018 - 2017

= 2017(2018 - 1)

= 2017×2017

= 2017²

Answer 2

$s = 2 + 4 + 6 + 8 + ... + 4034 - 2017 \\ s = 2(1 + 2 + 3 + ... +2017) - 2017 \\ s = 2( \frac{2017 \times 2018}{2} ) - 2017 \\ se \: taie \: 2 \: de \: la \: inceputul \: parantezei \: cu \: numitorul \: din \: fractie \\ s = 2017 \times 2018 - 2017 \\ s = 2017(2018 - 1) \\ s = 2017 \times 2017 \\ s = 2017 ^{2} \\ = > s \: este \: patrat \: perfect$