(a) Find an expression for the answer which is the sum of three terms involving binomial coefficients. (b) Find an expression for the answer which is the difference of two binomial coefficients. 0 1. COUNTING (c) Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle,

(a) Find an expression for the answer which is the sum of three terms involving binomial coefficients. (b) Find an expression for the answer which is the difference of two binomial coefficients. 0 1. COUNTING (c) Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle,

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.6: Binomial Theorem

Problem 48SE: Find (nk1)+(nk) and write the answer as a binomial coefficient in the form (nk) . Prove it. Hint:Use...

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Find (nk1)+(nk) and write the answer as a binomial coefficient in the form (nk) . Prove it. Hint:Use the fact that, for any integer p, such that p1 , p!=p(p1)! .
Use the Binomial Theorem to write the first three terms of (2a+b)17.

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