Answer
See explanation.
Work Step by Step
(a) Not valid. For example, $1=a_{i}=b_{i}$ for all $i .$ And then $\sum_{i=1}^{n} a_{i} b_{i}=n$ and $\sum_{i=1}^{n} a_{i} \sum_{i=1}^{n} b_{i}=n \cdot n=n^{2}$
(b) Not valid. For example, 1= $a_{i}$ for all $i .$ And then $\sum_{i=1}^{n} a_{i}^{2}=n$ and $\left(\sum_{i=1}^{n} a_{i}\right)^{2}=n^{2}$
(c) Not valid. For example, $a_{i}=b_{i}=1$ for all $i .$And then $\sum_{i=1}^{n} \frac{a_{i}}{b_{i}}=n$ and $\frac{\sum_{i=1}^{n} a_{i}}{\sum_{i=1}^{n} b_{i}}=\frac{n}{n}=1$
(d) Valid. Let $i=j+1,$ and then $i=1$. j must equal zero, and $i=n$ if and only if $-1+n=j$
