Interactive Real Analysis
- part of Lemma: Summation by Parts
Consider the two sequences
and
.
Let
S N =
be the n-th partial sum. Then for any
0 
m
n
we have:
Context
and
.
Let
S N =
be the n-th partial sum. Then for any
0 m
n
we have:
ContextProof
The proof is simply a calculation, where the various sums are carefully reindexed:
