In the series AABABCABCDABCDE... which letter occupies the 100th position?

The series is organized into segments of increasing length. The first segment is A (1 letter). The second segment is AB (2 letters). The third segment is ABC (3 letters). The nth segment has n letters.

To find the 100th position, we sum the number of letters in each segment until we get close to 100. The sum of the first n integers is calculated as n multiplied by n plus 1, divided by 2.

For n equal to 13: 13 multiplied by 14 divided by 2 equals 91. This means that after 13 complete segments (ending with M), 91 positions are filled.

To reach the 100th position, we need 9 more letters in the 14th segment. The 14th segment starts: 1st: A 2nd: B 3rd: C 4th: D 5th: E 6th: F 7th: G 8th: H 9th: I

The 9th letter of the 14th segment is I, which corresponds to the 100th position in the series. Therefore, the correct option is B.