   Chapter 9.7, Problem 54ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Express each of the sums in 43-54 in closed form (without using a summation symbol and without using an ellipsis…). ∑ k = 0 n ( − 1 ) k ( k n ) 3 2 n − 2 k 2 2 k

To determine

Express the sum k=0n(1)k(nk)32n2k22k in closed form (without using a summation symbol and without using an ellipsis…).

Explanation

Given information:

k=0n(1)k(nk)32n2k22k

Calculation:

Consider; 3222=3222.

( 3 2 2 2 ) n = ( 3 2 2 2 ) n

( n 0 ) ( 3 2 ) n ( 2 2 ) 0 +( n 1 ) ( 3 2 ) n1 ( 2 2 ) 1 +( n 2 ) ( 3 2 ) n2 ( 2 2 ) 2 ++( n n ) ( 3 2 ) 0 ( 2 2 ) n = ( 94 ) n

( 1 )

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