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.