#### To determine

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

#### Explanation

**Given:**

The series
∑n=1∞bn
is divergent.

**Result used:**

If
∑n=1∞an
and
∑n=1∞bn
is convergent series then
∑n=1∞(an−bn)=∑n=1∞an−∑n=1∞bn
.

**Proof:**

Suppose the series
∑n=1∞(an+bn)
is convergent.

Here,
∑n=1∞(an+bn)
and
∑n=1∞an
are convergent.

Thus, by Result stated above ,
∑n=1∞(an+bn)−∑n=1∞an=∑n=1∞(an+bn−an)
is convergent.

Since,
∑n=1∞an+bn−∑n=1∞an
is convergent, it can be concluded that
∑n=1∞bn
is convergent.

This is contradiction to the series
∑n=1∞bn
is divergent.

Hence, the series
∑n=1∞(an+bn)
is divergent.