AABABCABCDABCDE... which letter occupies 100th position?

We'll, it is easy! I've explained above that the letter D
corresponds to the 10th position in this series of
letter.

Since the sum 1 + 2 + 3 + ... + 13 + 14 yields 105,
which is larger than 100, then the ultimate group of letters
is:

(A)(AB)(ABC)(ABCD)(ABCDE)....(ABCDEFGHIJKLM)(ABCDEFGHI)

Therefore
the letter M is located on the 91st position. From here, we'll start another sequence
and we'll count A=92, B=93,
C=94,D=95,E=96,F=97,G=98,H=99,I=100.

Logically, that's why
the letter I is located on the 100th position.