(4) Suppose series \sum_{k=1}^{\infty} a_{k}, a_{k} \geq 0 is convergent. For each of the following series, either show that it is convergent, or give an example that is divergent. \text

{ (a) } \sum_{k=1}^{\infty} \frac{a_{k}^{2}}{a_{k}+\frac{1}{k}} \text { (b) } \sum_{k=1}^{\infty} k a_{k}^{2} \text { (c) } \sum_{k=1}^{\infty} \frac{\left(1+\frac{1}{k}+a_{k}\right)^{4}-1}{k+a_{k}} \text { (d) } \sum_{k=1}^{\infty} \sqrt{\frac{a_{k}}{k}} \text { . }