## Multivariable Calculus, 7th Edition

a) The two sums are the same in what they represent, but they differ in indices. They both represent a summation of $n$ terms of the sequence $a_{i}$ or $a_{j}$ which looks like the following: $a_{1}$+$a_{2}$+$a_{3}$ +...+$a_{n}$ = $\Sigma a_{x}$, here $x$ is either $i$ or $j$ . b) The first notation means the same as part a, being the following: $a_{1}$+$a_{2}$+$a_{3}$ +...+$a_{n}$ = $\Sigma a_{i}$ , that is, the sum of all terms of $a_{i}$ which is influenced by the index i progressing from $1$ to $n$. On the other hand, the notation where the term is $a_{j}$ but the index of the summation symbol is $i$ starting from $1$ going to $n$ is equal to $n*a_{j}$ .