![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://i.redd.it/h3weisivdaf81.jpg)
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
![SOLVED: Theorem 2.4.6 Cauchy Condensation Test): Suppose (bn) is decreasing and satisfies bn > 0 for all n € N. Then, the series CA=1bn converges if and only if the series 2"b2" SOLVED: Theorem 2.4.6 Cauchy Condensation Test): Suppose (bn) is decreasing and satisfies bn > 0 for all n € N. Then, the series CA=1bn converges if and only if the series 2"b2"](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 CA=1bn converges if and only if the series 2"b2"
![Help Please - Proving a result using Cauchy's Condensation Test and p series. (Senior Undergraduate Analysis) : r/learnmath Help Please - Proving a result using Cauchy's Condensation Test and p series. (Senior Undergraduate Analysis) : r/learnmath](https://external-preview.redd.it/HkGjFhUttsyDMpMfXeu5_Ers_id74z-6kHNGd6JE1Jo.jpg?auto=webp&s=4fc19c9d59c6619705086af4e88dfa261e372ae7)