This paper gives a necessary and sufficient condition in order that a series
∑
a
n
ε
n
\sum {{a_n}} {\varepsilon _n}
should be summable
|
R
,
q
n
|
|R,{q_n}|
whenever
∑
a
n
\sum {{a_n}}
is summable
|
R
,
p
n
|
k
,
k
⩾
1
|R,{p_n}{|_k},\;k \geqslant 1
, and so extends the known result of Bosanquet to the case
k
>
1
k > 1
.