Hi Clive,
Clive wrote: I call it a shell...zillions of them among the sands of Florida.

is something similar to this what you mean?

[(3 + x)^(-1), {x, -6.1, 0.06}]

[(3 + x)^(-1), {x, -18, 12}]

1/3-x/9+x^2/27-x^3/81+x^4/243-x^5/729+x^6/2187-x^7/6561+x^8/19683-x^9/59049+x^10/177147-x^11/531441+x^12/1594323-x^13/4782969+x^14/14348907-x^15/43046721+x^16/129140163-x^17/387420489+x^18/1162261467-x^19/3486784401+x^20/10460353203+O(x^21)

[x, 0, {1/3, -1/9, 1/27, -1/81, 1/243, -1/729, 1/2187, -1/6561, 1/19683, -1/59049, 1/177147, -1/531441, 1/1594323, -1/4782969, 1/14348907, -1/43046721, 1/129140163, -1/387420489, 1/1162261467, -1/3486784401, 1/10460353203}, 0, 21, 1]

1/(3+x) = sum_(n=0)^infinityx^n (-1)^n 3^(-1-n) for |x|<3

Regards,
Jacob