I do not understand a small step in a proof I'm reading at the moment. Why are the following things equal?
n∑k=112k−1−12n∑k=11k=2n∑k=11k−n∑k=11k
Answer
Separating out the odd & the even terms in the denominator,
2n∑k=11k=n∑k=1(12k−1+n∑k=112k)
=n∑k=112k−1+n∑k=112k
=n∑k=112k−1+12n∑k=11k
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