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Q. 58

Found in: Page 327


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Given a simple proof that k=5n(ak+bk)=k=5nak+k=5nbk

We prove the statement k=5n(ak+bk)=k=5nak+k=5nbk

See the step by step solution

Step by Step Solution

Step 1: Given information

We are given a relation

k=5n(ak+bk)=k=5nak+k=5nbk. We have to prove this

Step 2: Proof

Consider LHS

We have,

k=5n(ak+bk) =(a5+b5)+(a6+b6)+....+(an+bn) =(a5+a6+...+an)+(b5+b6+....+b5) =k=5nak+k=5nbk=RHS

Hence proved

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