[tex]2 + 4 + 6 + ... + 400 = \\ 2 \times (1 + 2 + 3 + ...200) = \\ 2 \times \frac{200 \times 201}{2} = \\ = 200 \times 201[/tex]
[tex]4 + 8 + 12 + ... + 100 = \\ 4 \times (1 + 2 + 3 + ... + 25) = \\ 4 \times \frac{25 \times 26}{2} = \\ = 2 \times 25 \times 26[/tex]
[tex](2 + 4 + 6 + ... + 400) \div (4 + 8 + 12 + ... + 100) = \\ \frac{200 \times 201}{2 \times 25 \times 26} = \frac{4 \times 201}{26} = \frac{2 \times 201}{13} = \frac{402}{13} [/tex]
