The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?	Options.
A) 101! B) 100! C) 99^2(98!) D) 100^2(99!) E) (100!)2
According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out:   101! - 100!   Both these terms have something in common: 100! so we can factor that out of each piece...   101! - 100!   100!(101 - 1)   Simplifying the parentheses, we get...   100!(100)   Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices...   100! = (100)(99!) so our answer can be rewritten as...   (100)(99!)(100)   Or....   (100^2)(99!)   ANSWER:100^2(99!)
<result>D</result>
The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?