Word Count : 273

---

We will first express \( x^5 \) in terms of falling factorials and then evaluate the Stirling numbers of the second kind, \( S_5^m \), for \( m = 0,1,2,3,4,5 \). ### Step 1: Express \( x^5 \) in Terms of Falling Factorials The falling factorial is defined as: \[ (x)_m = x (x-1) (x-2) \dots (x-m+1) \] Any power \( x^n \) can be rewritten as a __________ ___ ___ _____ ________ ______.
_______ _____ ________ ____ _______ ________ ___ ___ ____ _________.
____ __________ ________ ______ _______ _______ _______ __________.
____ __________ ____ _____ _________ ___.
_____ _____ ____ ______ _______ _________ ________ ______ ___ ____ ______ ___.
___ ___ _____ ______ _______ _____ _______ __________.
______ ______ _____ _________ ____ ________ ________ _______ _______ _________ ___ __________.
______ __________ ________ __________ _________ ________ _______ _____.
_______ ____ ______ _________ ______ _______ ______ ____ ______ __________ ___.
_______ ______ _____ _________ ___ ______ ______ ______ ___ _________ __________.
___ ________ _____ ___ ________ ____ _____ __________ _____.
_________ _________ _________ _____ ____.
____ _______ ___ ______ ________ ________ _________ __________ ______ ________ _____.
________ _____ __________ ___ ____ __________ ________ ___.
__________ __________ _____ ___ ____ _____ _______.
____ _______ _______ ___ ____ _____ _______ ________ _______ ___ __________.
__________ _________ ___ __________ _________ ________ _____ _________.
__________ ________ ___ _______ _____ _________ ________ _________ _______.
__________ _____ __________ ___ ____ __________ ___ _______ ___.
________ __________ ___ ______ ______ _______ _________ _______ _________ ______ ______.
______ ___ __________ ___ _____ _______ _________ _______.
________ __________ ________ _________ _________ ____ __________ __________.
__________ ____ ______ ________ ______ _________ ______.
____ _________.
Get Full Answer on WhatsApp