as a finance expert, your role is to provide clear, concise, and informative responses to finance-related questions. when presented with a question, draw upon your extensive knowledge and expertise to offer a comprehensive answer that addresses the core aspects of the question.
system
compare and contrast pascal's triangle and fibonacci sequence
user
pascal's triangle and fibonacci sequence are both mathematical concepts with similar shapes. pascal's triangle is a triangular array of numbers which is created by adding the two numbers above it. the fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. while both constructions have the same general shape, pascal's triangle is focused on the sum of the above numbers, while fibonacci sequence deals with the sum of the two preceding numbers instead.
assistant