Modified pyramids

Algebra Level 2

131+35+71+3+57+9+111+3+5+79+11+13+151+3+5+7+911+13+15+17+19\large \begin{array} {c c c c c c c } & 1 & & & & & & 3 \\ & 1+ 3 & & & & & & 5 + 7 \\ & 1 + 3 + 5 & & & & & & 7 + 9 + 11 \\ & 1 + 3 + 5 + 7 & & & & & & 9 + 11 + 13 + 15 \\ & 1 + 3 + 5 + 7 + 9 & & & & & & 11 + 13 + 15 + 17 + 19 \\ & \dots & & & & & & \ldots \\ & \dots & & & & & & \ldots \\ & \dots & & & & & & \ldots \\ \end{array}

Let ana_n denote the sum of the first nn positive odd numbers and bnb_n as the sum of the next nn positive odd numbers. Above shows the first 5 rows of ana_n and bnb_n respectively. What is the value of

b100÷a100? \large b_{100} \div a_{100} ?

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