[tex]a)a = 2017 + 2(1 + 2 + ... + 2016)[/tex]
[tex]a = 2017 + 2 \times \frac{2016(2016 + 1)}{2} [/tex]
[tex]a = 2017 + 2016(2016 + 1)[/tex]
[tex]a = 2017 + 2016 \times 2017[/tex]
[tex]a = 2017(1 + 2016)[/tex]
[tex]a = 2017 \times 2017[/tex]
[tex]a = {2017}^{2} = > p.p[/tex]
[tex]b)b = 1 + 3 + 5 + ... + 2017[/tex]
[tex]1 + 3 + 5 + ... + 2n - 1 = {n}^{2} [/tex]
[tex]2n - 1 = 2017[/tex]
[tex]2n = 2017 + 1[/tex]
[tex]2n = 2018 \: | \div 2[/tex]
[tex]n = 1009[/tex]
[tex] {n}^{2} = {1009}^{2} = > p.p[/tex]
[tex]c)c = 81 + 2 \times 81 + 3 \times 81 + ... + 49 \times 81[/tex]
[tex]c = 81(1 + 2 + 3 + ... + 49)[/tex]
[tex]c = 81 \times \frac{49(49 + 1)}{2} [/tex]
[tex]c = 81 \times \frac{49 \times 50}{2} [/tex]
[tex]c = 81 \times 49 \times 25[/tex]
[tex]c = {9}^{2} \times {7}^{2} \times {5}^{2} [/tex]
[tex]c = {(9 \times 7 \times 5)}^{2} = > p.p[/tex]
[tex]d)d = 2(1 + 2 + 3 + ... + 124) + 125[/tex]
[tex]d = 2 \times \frac{124(124 + 1)}{2} + 125[/tex]
[tex]d = 124(124 + 1) + 125[/tex]
[tex]d = 124 \times 125 + 125[/tex]
[tex]d = 125(124 + 1)[/tex]
[tex]d = 125 \times 125[/tex]
[tex]d = {5}^{3} \times {5}^{3} [/tex]
[tex]d = {(5 \times 5)}^{3} [/tex]
[tex]d = {25}^{3} = > c.p[/tex]
