4. Prove that for any positive integer n, if ao,a1,.…..,an is a sequence of real numbers and ce R, then L Ec.ai C. ai = i=0 i=0 Section 5.7
4. Prove that for any positive integer n, if ao,a1,.…..,an is a sequence of real numbers and ce R, then L Ec.ai C. ai = i=0 i=0 Section 5.7
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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![**Problem Statement:**
4. Prove that for any positive integer \( n \), if \( a_0, a_1, \ldots, a_n \) is a sequence of real numbers and \( c \in \mathbb{R} \), then
\[
c \cdot \sum_{i=0}^{n} a_i = \sum_{i=0}^{n} c \cdot a_i
\]
**Section 5.7**
(Note: No diagrams or graphs are present in the image provided.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46c0fb16-724b-4726-818c-9156075ac6cc%2Fc64aad4d-712d-419e-88c5-d4d246304021%2F3ujozi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
4. Prove that for any positive integer \( n \), if \( a_0, a_1, \ldots, a_n \) is a sequence of real numbers and \( c \in \mathbb{R} \), then
\[
c \cdot \sum_{i=0}^{n} a_i = \sum_{i=0}^{n} c \cdot a_i
\]
**Section 5.7**
(Note: No diagrams or graphs are present in the image provided.)
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