An easy way that an infinite series can converge is if all the a are zero for n sufficiently large.
The building had a large "N" painted on the roof.
The behavior for large n is of primary interest.
For large n, a number of asymptotic formulae are known.
The copy referred to is marked with a large N in red, with an eagle's head.
Often and it is required that each have a certain property for n sufficiently large.
In other words, for large n, the effect of the prior probability on the posterior is negligible.
For large N (and the practical requirements of a phone switch are considered large) this growth was too expensive.
For large n the levels are almost never occupied and then only temporarily.
For a large N the difference is negligible.