#### 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+122+133+144+155+...
.

The given series can be written as follows,

1+122+133+144+155+...=∑n=1∞1nn=∑n=1∞1n⋅n12=∑n=1∞1n1+12=∑n=1∞1n32

Clearly, the above series is *p-*series with
p=32
.

Here,
p>1
.

Use the Result stated above, it can be conclude that the given series is convergent.