The given series is: AABABCABCDABCDE…

The pattern follows: A, AB, ABC, ABCD, ABCDE, and so on, where the number of letters increases in an arithmetic progression. We need to determine how many such terms fit within a total of 100 letters.

In an arithmetic series, the sequence is 1, 2, 3, ..., where the sum of the first $n$ terms can be calculated using the formula: Sum=$(\frac{n}{2})(n+1)$

To find $n$ such that the total number of letters is at least 100, we need to solve: $(\frac{n}{2})(n+1) \ge 100$

Estimating this, we find that $n = 14$ is the largest integer satisfying this condition.

Calculating for $n = 13$: Sum=$(\frac{13 \times 14}{2})=91$

This means that the 13th block ends at the 91st letter. The letters for the 14th block (which starts at position 92) are: 92nd: A, 93rd: B, ... , 100th: I

Thus, the letter at the 100th position is I.