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?