A particle detector records decay events in successive half-life bins

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Foundations of mathematical language · Foundations of mathematical language

Mathematical Methods for Physics, Ch Series, limits and controlled approximation

Problem

A particle detector records decay events in successive half-life bins. The weighted total number of counts is modelled as the series N=∑n=1∞n2n.N = \sum_{n=1}^{\infty} \frac{n}{2^n}. Decide whether this series converges, naming the test used and showing the comparison or limit that settles it.

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