#### To determine

**To prove:** The series
∑n=1∞can
is divergent.

#### Explanation

**Given:**

The series
∑n=1∞an
is divergent.

**Result used:**

A series
∑n=1∞an=a1+a2+a3+⋯
and
sn=∑i=1nai=a1+a2+a3+⋯+an
.

If the sequence
{sn}
is divergent then the series
∑n=1∞an
is divergent.

**Proof:**

Consider the series
∑n=1∞an
is divergent.

That is, the
∑n=1∞an
series is not finite.

Therefore,
c∑n=1∞an
is also not finite.

Note that,
c∑n=1∞an=∑n=1∞can
.

Hence, the series
∑n=1∞can
is divergent.