FWIW,
Although Maple 11.01 seems to be correctly installed on my Windows box (kernelopts(version) is in agreement with what is displayed in the dialog box Help -> About Maple...), I still do not get DJKeenan's results: f does not evaluate to infinity when _EnvFormal is not set, and g with k == 5 evaluates to the erroneous 2.700548143. (The code below ran from a fresh session.)

> kernelopts(version);
Maple 11.01, IBM INTEL NT, Jun 8 2007 Build ID 296069
> f := proc (k) options operator, arrow; sum((1+exp(n))/(exp(n)-1),
n = k .. infinity) end proc;
seq(f(i), i = 1 .. 9);
infinity
-----
\
) 1 + exp(n)
k -> / ----------
----- exp(n) - 1
n = k
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 1 n = 2 n = 3
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 4 n = 5 n = 6
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 7 n = 8 n = 9
> _EnvFormal := true;
seq(f(i), i = 1 .. 9);
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 1 n = 2 n = 3
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 4 n = 5 n = 6
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 7 n = 8 n = 9
> g := proc (k) options operator, arrow; evalf(Sum((1+exp(n))/(exp(n)-1),
n = k .. infinity)) end proc;
seq(g(i), i = 1 .. 9);
/infinity \
| ----- |
| \ |
| ) 1 + exp(n)|
k -> evalf| / ----------|
| ----- exp(n) - 1|
\ n = k /
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 1 n = 2 n = 3
infinity infinity infinity
----- ----- -----
\ \ \
) 1 + exp(n) ) 1 + exp(n) ) 1 + exp(n)
/ ----------, 2.700548143, / ----------, / ----------,
----- exp(n) - 1 ----- exp(n) - 1 ----- exp(n) - 1
n = 4 n = 6 n = 7
infinity infinity
----- -----
\ \
) 1 + exp(n) ) 1 + exp(n)
/ ----------, / ----------
----- exp(n) - 1 ----- exp(n) - 1
n = 8 n = 9

Regards,
--
Jean-Marc