In: Advanced Math
Prove that if ∑an converges absolutely, then both ∑Pn and ∑Nn converge
If
converges absolutely then series
converges.
are positive terms of series
and
are negative terms of series
.
Since series
and
both converges.
Therefore, their sum
also converges
=>
also converges
=>
converges
Similarly, as
and
converges.
Therefore,
also converges
=>
also converges.
=>
converges.
Hnece,
and
converges if
converges absolutely.