If
diverges and
Show that :
The series
diverges also.
First I thought about nth terms test, but it failed.
since
can be zero.
Then:
I cosidered that sequence of the partial sums for the first seires
Since the series diverges, then {
} diverges.
i.e.
,
or D.N.E
The sequence of partial sums for the second series , denotes by
, is
Clearly:
if
then
depending on the sign of
Hence, The series
diverges.
But what if
D.N.E ?
i.e. If you multiply a D.N.E Limit with by a constant, It will be D.N.E too ?
My proof is right?