#### To determine

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

#### Explanation

**Result used:**

(1) If the series
∑n=1∞an
is convergent, then
limn→∞an=0
.

(2) If the limit does not exist or
limn→∞an≠0
, then the series
∑n=1∞an
is divergent.

**Proof:**

Consider the given series
∑n=1∞an
is convergent.

Thus, by Result (1) stated above,
limn→∞an=0
.

Since
limn→∞an=0
,
limn→∞1an=∞
.

That is,
limn→∞1an≠0

Thus, by Result (2) stated above, the series
∑n=1∞1an
.is divergent.

Hence, the required result.