How to write this expression in sigma notation?

Question

Write this expression in sigma notation:

$$\frac 1{2k} + \frac 2{3k} + \frac 3{4k} + \ldots + \frac{k-1}{k^2} + \frac 1{k+1}.$$

Answer 1

$$\sum\limits_{i=1}^k \dfrac i {(i+1)k}$$

(Note that when $i=k-1$ the summand simplifies to $\dfrac{k-1}{k^2}$,

and when $i=k$ the summand simplifies to $\dfrac1{k+1}$.)