A series ∑ UN converges. How can we prove that its odd term ∑ u2n-1 also converges?

A series ∑ UN converges. How can we prove that its odd term ∑ u2n-1 also converges?

Because the series converges, let
ΣUn=A.
When n tends to infinity, all 2N-1 values can be obtained
therefore
ΣU2n-1=A.
It has been proved