#### To determine

**To describe:** The series
∑n=1∞(an+bn)
necessarily divergent.

#### Answer

No, the series
∑n=1∞(an+bn)
is not necessarily a divergent series.

#### Explanation

**Given:**

The series
∑n=1∞an
and
∑n=1∞bn
are divergent.

**Example:**

Consider the series
∑n=1∞an=∑n=1∞n and ∑n=1∞bn=∑n=1∞−n
both are divergent series.

Obtain the series
∑n=1∞(an+bn)
.

∑n=1∞(an+bn)=∑n=1∞(n+(−n))=∑n=1∞(n−n)=0

The series
∑n=1∞an+bn
is not necessarily a divergent series.