1+3+5+7+..+99=(2×0+1)+(2×1+1)+(2×2+1)+...+(49×2+1)= 2(0+1+2+3+..49)+1×50=
[tex]2 \times \frac{49 \times 50}{2} + 50 = 49 \times 50 + 50 = 50 \times (49 + 1) = 50 \times 50[/tex]
[tex]1+2+3+4+...+100 = \frac{100 \times 101}{2} = 50 \times 101[/tex]
[tex] \frac{50 \times 101}{50 \times 50} = \frac{101}{50} [/tex]
