Answer
Please see step-by-step
Work Step by Step
Let the sequence $\{a_{n}\}=a_{1},a_{2},a_{3},\cdots$
Then, applying the subscript index,
(a) $\quad \displaystyle \sum_{n=1}^{\infty}a_{n}=a_{1}+a_{2}+a_{3}+\cdots$
(b)$\displaystyle \quad\sum_{k=1}^{\infty}a_{k}=a_{1}+a_{2}+a_{3}+\cdots$
(c)$\displaystyle \quad\sum_{n=1}^{\infty}a_{k}=a_{k}+a_{k}+a_{k}+\cdots=a_{k}(1+1+1+...)$
So, (a) and (b) are equal
(c) is different to (a) and (b), unless the sequence $\{a_{n}\}$ has all terms equal,
$\{a_{n}\}$=$a_{k},a_{k},a_{k}....$
