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Advanced Engineering Mathematics
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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Step 1

To prove: ∑j=1nj=1+2+3+4+⋯+n=nn+12

We prove this by Mathematical Induction.

 

Basis step: Prove the result for n = 1.

LHS=∑j=11j=1RHS=11+12=22=1LHS=RHS

The result is true for n = 1.

 

Inductive hypotheses: The result is true for k, where 1≤k≤n.

∑j=1kj=1+2+3+⋯+k=kk+12

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