To determine which letter occupies the 100th position in the given series AABABCABCDABCDE..., let`s break down the pattern and analyze it step by step.

The series starts with the letter `A`. Then, it repeats the pattern of adding a new letter and incrementing the number of letters in each subsequent segment. Let`s break it down:

Segment 1: A

Segment 2: AB

Segment 3: ABC

Segment 4: ABCD

Segment 5: ABCDE

From this breakdown, we can observe a few patterns:

1. The length of each segment corresponds to the segment number. For example, Segment 1 has 1 letter, Segment 2 has 2 letters, and so on.

2. The letters in each segment are derived from the alphabets. Segment 1 has `A`, Segment 2 has `A` and `B`, Segment 3 has `A`, `B`, and `C`, and so on.

To determine the position of a specific letter, we need to identify the segment it belongs to and its position within that segment.

Let`s calculate the position of the 100th letter step by step:

Segment 1 has 1 letter (A). The total number of letters covered so far is 1.

Segment 2 has 2 letters (A, B). The total number of letters covered now is 1 + 2 = 3.

Segment 3 has 3 letters (A, B, C). The total number of letters covered is 3 + 3 = 6.

Segment 4 has 4 letters (A, B, C, D). The total number of letters covered is 6 + 4 = 10.

Segment 5 has 5 letters (A, B, C, D, E). The total number of letters covered is 10 + 5 = 15.

At this point, we have covered 15 letters. To find the segment that contains the 100th letter, we need to determine which segment covers the 100th letter.

Since the pattern repeats, we can subtract the total number of letters covered (15) from 100 to find how many letters are left:

100 - 15 = 85

Now, we need to find the segment that covers the 85th letter. To do this, we find the segment number that corresponds to or is greater than 85.

Segment 6 has 6 letters (A, B, C, D, E, F). The total number of letters covered is 15 + 6 = 21.

Segment 7 has 7 letters (A, B, C, D, E, F, G). The total number of letters covered is 21 + 7 = 28.

Segment 8 has 8 letters (A, B, C, D, E, F, G, H). The total number of letters covered is 28 + 8 = 36.

Segment 9 has 9 letters (A, B, C, D, E, F, G, H, I). The total number of letters covered is 36 + 9 = 45.

Segment 10 has 10 letters (A, B, C, D, E, F, G, H, I, J). The total number of letters covered is 45 + 10 = 55.

Segment 11 has 11 letters (A, B, C, D, E, F, G, H, I, J, K). The total number of letters covered is 55 + 11 = 66.

Segment 12 has 12 letters (A, B, C, D, E, F, G, H, I, J, K, L). The total number of letters covered is 66 + 12 = 78.

Segment 13 has 13 letters (A, B, C, D, E, F, G, H, I, J, K, L, M). The total number of letters covered is 78 + 13 = 91.

Segment 14 has 14 letters (A, B, C, D, E, F, G, H, I, J, K, L, M, N). The total number of letters covered is 91 + 14 = 105.

At this point, we have covered 105 letters. Since we have surpassed the 100th position, we can determine that the 100th position falls within Segment 14.

To determine the exact letter at the 100th position, we need to find the relative position within Segment 14. The 100th position is 100 - 91 = 9 positions into Segment 14.

Segment 14 contains the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N. Counting 9 positions from the start of this segment, we find that the letter at the 100th position is `I`.

Therefore, the answer is Option 2: I.

By analyzing the pattern and calculating the position step by step, we determined that `I` is the letter occupying the 100th position in the series AABABCABCDABCDE...