BUG: Fix np.inf + np.nan sum issue on groupby mean

pandas/_libs/groupby.pyx

@@ -54,6 +54,8 @@ cdef int64_t NPY_NAT = util.get_nat()
 
 cdef float64_t NaN = <float64_t>np.NaN
 
+cdef float64_t Infinity = <float64_t>np.Inf
+
 cdef enum InterpolationEnumType:
     INTERPOLATION_LINEAR,
     INTERPOLATION_LOWER,
@@ -1073,7 +1075,10 @@ def group_mean(
                 if not isna_entry:
                     nobs[lab, j] += 1
                     y = val - compensation[lab, j]
-                    t = sumx[lab, j] + y
+                    if sumx[lab, j] == Infinity:
+                        t = Infinity
+                    else:
+                        t = sumx[lab, j] + y
                     compensation[lab, j] = t - sumx[lab, j] - y
                     sumx[lab, j] = t