Question

Să se calculleze suma numerelor : S=(2x1+1)+(2x2+1)+(2x3+1)........+(2x100+1)

Answer 1

$S = (2 \times 1 + 1) + (2 \times 2 + 1) + (2 \times 3 + 1) + ... + (2 \times 100 + 1)$

$S = 3 + 5 + 7 + ... + 201$

$3 + 5 + 7 + ... + 2n - 1 = {n}^{2}$

$2n - 1 = 201$

$2n = 201 + 1$

$2n = 202 \: | \div 2$

$n = 101$

${n}^{2} = {101}^{2} = 10201$

$= > S = 10201$