You have been provided with the following mathematical expressions. Which of them has the solution of 1 numerically? A. [n] at n=1-5 B. {S[n+1] n=0 80 c. 8[n-1] h=0 ∞ D. 2-6 CM 82-6 [n]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You have been provided with the following mathematical expressions. Which of them has the
solution of 1 numerically?
A. S[n] at n=1-5
B. [S[n+1]
00
n=0
c. [8[n-1]
h=0
∞0
D. Σ 2.8 [n]
n2-00
Transcribed Image Text:You have been provided with the following mathematical expressions. Which of them has the solution of 1 numerically? A. S[n] at n=1-5 B. [S[n+1] 00 n=0 c. [8[n-1] h=0 ∞0 D. Σ 2.8 [n] n2-00
Expert Solution
Step 1: define Problem

A. delta open square brackets 1.5 close square brackets space equals 0.

B. sum from 0 to infinity of delta open square brackets n plus 1 close square brackets equals 0.

C. sum from 0 to infinity of δ[n-1] =1

Proof: The delta function evaluates to 1 when its argument is 0 and 0 otherwise. In this case, the argument of δ[n-1] becomes 0 when n = 1 and is non-zero for all other values of n.

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