Question

va rog sa ma ajutati la acest exercitiu URGENT

Answer 1

$a)a = 2017 + 2(1 + 2 + ... + 2016)$

$a = 2017 + 2 \times \frac{2016(2016 + 1)}{2}$

$a = 2017 + 2016 (2016 + 1)$

$a = 2017 + 2016 \times 2017$

$a = 2017(1 + 2016)$

$a = 2017 \times 2017$

$a = {2017}^{2} = > p.p$

$b)b = 1 + 3 + 5 + ... + 2017$

$1 + 3 + 5 + ... + 2n - 1 = {n}^{2}$

$2n - 1 = 2017$

$2n = 2017 + 1$

$2n = 2018 \: | \div 2$

$n = 1009$

${n}^{2} = {1009}^{2}$

$b = {n}^{2} = {1009}^{2} = > p.p$

$c)c = 81 + 2 \times 81 + 3 \times 81 + ... + 49 \times 81$

$c = 81(1 + 2 + 3 + ... + 49)$

$c = 81 \times \frac{49(49 + 1)}{2}$

$c = 81 \times \frac{49 \times 50}{2}$

$c = 81 \times 49 \times 25$

$c = {9}^{2} \times {7}^{2} \times {5}^{2}$

$c = {(9 \times 7 \times 5)}^{2} = > p.p$

$d)d = 2(1 + 2 + 3 + ... + 124) + 125$

$d = 2 \times \frac{124(124 + 1)}{2} + 125$

$d = 124(124 + 1) + 125$

$d = 124 \times 125 + 125$

$d = 125(124 + 1)$

$d = 125 \times 125$

$d = {5}^{3} \times {5}^{3}$

$d = {(5 \times 5)}^{3}$

$d = {25}^{3} = > c.p$