#### To determine

Whether the series is convergent or divergent and obtain the sum if the series is convergent.

#### Answer

The series is divergent.

#### Explanation

**Given:**

The series is
13+16+19+112+115+⋯
.

**Recall:**

Harmonic series
∑n=1∞1n=1+12+13+14+15+⋯
is divergent. (1)

**Calculation:**

Consider the given series.

13+16+19+112+115+⋯=13⋅1+13⋅2+13⋅3+13⋅4+13⋅5+⋯=13⋅11+13⋅12+13⋅13+13⋅14+13⋅15+⋯=13⋅(11+12+13+14+15+⋯)=13⋅∑n=1∞1n

Here,
∑n=1∞1n
is harmonic series and by equation (1), it is divergent.

Thus,
13⋅∑n=1∞1n
is also divergent.

Therefore, it can be concluded that the given series is divergent.