Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 41

41
1
(1 — x)
we have therefore:
(71+ 1)X"=
„ = o (!-x)
(80)
for all values of x while
(n + 1) x" =---------—~
lim (/;+l)x — (n + 2)x
n 00 (1 — X)2
,» + 1
(81)
From the definition of it will be apparent that this
sign does not signify an ordinary summation, rather we
may consider it as a sign of a special mafhematical ope-
ration. I have, therefore, formerly used the sign $ to denote
this operation, in order to emphasize its difference from
common summation. In present paper I have, however,
found it more practical to use^> to make it clearthat one
of the most prominent caracteristics of the operation con-
cerned is its additive nature, manifesting itself among other
things by the fact that we can sum up a certain number
of the first terms and get the exact result by adding a
iemainder term to the sum thus obtained.
I maintain that the introduction of the infinite series
cxo
'y anx'1 as different from ^> anx" constitutes a considerable
n=0 n =o
advantage in mathematical operations. As already pointed