[tex]S = (2 \times 1 + 1) + (2 \times 2 + 1) + (2 \times 3 + 1) + ... + (2 \times 100 + 1)[/tex]
[tex]S = 3 + 5 + 7 + ... + 201[/tex]
[tex]3 + 5 + 7 + ... + 2n - 1 = {n}^{2} [/tex]
[tex]2n - 1 = 201[/tex]
[tex]2n = 201 + 1[/tex]
[tex]2n = 202 \: | \div 2[/tex]
[tex]n = 101[/tex]
[tex] {n}^{2} = {101}^{2} = 10201[/tex]
[tex] = > S = 10201[/tex]
