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Tuesday, November 22, 2016

Mathematical Analysis - Exercise 1.2

Problem:

Solution:

The right hand side sounds like something we can telescope, let's see:

(ab)n1k=0akbn1k=an1k=0akbn1kbn1k=0akbn1k=n1k=0ak+1bn1kn1k=0akbnk=(an+n2k=0ak+1bn1k)(n1k=1akbnk+bn)=(an+n1k=1akbnk)(n1k=1akbnk+bn)=anbn

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