1) Use Mathematical induction to show the following formula for all Σ (5; ² + j) = n²³² + 2n²+ n ST Base Case: We will show P(1) holds, If n=1, then (3(1) ²+1) = 1³ + 2(1)² + 1 (3+1) = 1+2+1 4=4 Thus P(1) holds Inductive Stepi P(n) holds that Pentil holds 021

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
1)
Use Mathematical induction to show the following formula for all nel
• Σ ² ( 3j²³+j) = n²³+ ²₁³² + n
3
2
Base Case:
We will show PC) holds, If n=1 then (3 (1) ² + 1) = 1³ + 2(1) ³² + 1
(3+1) = 1+2+1
4=4
Thus P(1) holds
Inductive Steps
Assume that P(n) holds, show that PCAHI) holds.
Transcribed Image Text:1) Use Mathematical induction to show the following formula for all nel • Σ ² ( 3j²³+j) = n²³+ ²₁³² + n 3 2 Base Case: We will show PC) holds, If n=1 then (3 (1) ² + 1) = 1³ + 2(1) ³² + 1 (3+1) = 1+2+1 4=4 Thus P(1) holds Inductive Steps Assume that P(n) holds, show that PCAHI) holds.
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