They are the best of series, they are the worst of series. One series converges for all z,
but often fails to provide meaningful numerical values. One series diverges for all z
yet often gives excellent numerical values. What the Dickens is going on?
The two series with the perplexing properties arise from an important problem,
finding the area under the normal distribution curve e.z2/2
ã
2ƒÎ
from z to infinity. Our first
series will be obtained using integration by parts in the next section