![SOLVED: The Cauchy condensation test says: Let {an} be a nonincreasing sequence (an ≥an+1 for all n) of positive terms that converges to 0 . Then ∑an converges if and only if SOLVED: The Cauchy condensation test says: Let {an} be a nonincreasing sequence (an ≥an+1 for all n) of positive terms that converges to 0 . Then ∑an converges if and only if](https://cdn.numerade.com/previews/fd379d03-849c-4c97-bf76-81d29b3f7db0.gif)
SOLVED: The Cauchy condensation test says: Let {an} be a nonincreasing sequence (an ≥an+1 for all n) of positive terms that converges to 0 . Then ∑an converges if and only if
![SOLVED: Theorem 2.4.6 (Cauchy Condensation Test): Suppose (bn) is decreasing and satisfies bn > 0 for all n ∈ N. Then, the series Σ(1/bn) converges if and only if the series Σ(2^nb2^n) SOLVED: Theorem 2.4.6 (Cauchy Condensation Test): Suppose (bn) is decreasing and satisfies bn > 0 for all n ∈ N. Then, the series Σ(1/bn) converges if and only if the series Σ(2^nb2^n)](https://cdn.numerade.com/ask_images/a64dbaa3107c41469b1713b3e1e29340.jpg)
SOLVED: Theorem 2.4.6 (Cauchy Condensation Test): Suppose (bn) is decreasing and satisfies bn > 0 for all n ∈ N. Then, the series Σ(1/bn) converges if and only if the series Σ(2^nb2^n)
![Why does m <= 2^(k+1) - 1 make sense in this proof of the Cauchy Condensation Test? I'm not sure where it comes from or why it works, it seems arbitrary. : r/askmath Why does m <= 2^(k+1) - 1 make sense in this proof of the Cauchy Condensation Test? I'm not sure where it comes from or why it works, it seems arbitrary. : r/askmath](https://preview.redd.it/h3weisivdaf81.jpg?width=1080&crop=smart&auto=webp&s=52fdda5db35fa0df1ff7585651de5931fd193da7)