Problem:
Solution:
The right hand side sounds like something we can telescope, let's see:
(a−b)n−1∑k=0akbn−1−k=an−1∑k=0akbn−1−k−bn−1∑k=0akbn−1−k=n−1∑k=0ak+1bn−1−k−n−1∑k=0akbn−k=(an+n−2∑k=0ak+1bn−1−k)−(n−1∑k=1akbn−k+bn)=(an+n−1∑k=1akbn−k)−(n−1∑k=1akbn−k+bn)=an−bn
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