#### To determine

Whether the series is convergent or divergent.

#### Answer

The series is convergent.

#### Explanation

**Result used**:

The
p
-series
∑n=1∞1np
is convergent if
p>1
and divergent if
p≤1
.

**Given:**

The series is
1+18+127+164+1125+...
.

**Calculation:**

The given series can be written as follows,

1+18+127+164+1125+...=1+123+133+143+153+...=∑n=1∞1n3

Clearly, the above series is
p
-series with
p=3>1
.

Use the Result stated above, it can be conclude that the given series
1+18+127+164+1125+...
is convergent.