Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches ...

Only some bats and toothed whales rely on sophisticated echolocation, in which they emit sonar pulses and process returning echoes, to detect and track down small prey. Now, two new studies show that ...

High-throughput sequencing of related individuals has become an important tool for studying human disease. However, owing to technical complexity and lack of available tools, most pedigree-based ...