any technique or "trick" for finding the coefficient


by davedave
Tags: coefficient, technique, trick
davedave
davedave is offline
#1
Nov8-09, 11:50 PM
P: 48
Here is the polynomial expression

(x+x^2+x^3+x^4+x^5+x^6)^5

Each x term is raised to ascending powers of 1.

The entire sum in the brackets is raised to the 5th power.

Does anyone have any "special trick" for finding the coefficient of the term which contains x^19?
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
fourier jr
fourier jr is offline
#2
Nov8-09, 11:56 PM
P: 943
what about generating functions? there's another way to rewrite the finite geometric series inside the brackets, and that formula raised to the 5th power has another formula, and you can plug in the appropriate numbers to get the coefficient for x^19
Gib Z
Gib Z is offline
#3
Nov9-09, 02:39 AM
HW Helper
Gib Z's Avatar
P: 3,353
Think about how would you write out the expansion normally? You would write out the 5 factors in 5 seperate brackets (..)(..)(..)(..)(..), and pick a term from each bracket to form a term on the RHS. How many ways can you pick those terms differently to get the exponents adding to 19? It's now a combinatorics problem.


Register to reply

Related Discussions
Newton's law "trick?" question Introductory Physics Homework 2
Difference between "Identical", "Equal", "Equivalent" Calculus & Beyond Homework 9
Time laspe "trick" for a plant/tree Biology 9
"Feynman integration trick" - textbooks? Calculus 13