WOLFRAM|DEMONSTRATIONS PROJECT

Series Expansion of 1/(1-x)

k

9

The plots are of

1/(1-x)

against the

th

k

partial sums of the two expansions:

|x|>1:-

-1

x

-

-2

x

-...

|x|<1:1+x+

2

x

+...

The first tends to

-∞

as

x1+

, the second to

+∞

as

x1-

, and both exhibit erratic behavior as

x-1

.