$$a_n = n\dfrac{n^2 + 5}{4}$$

In the above fraction series, for $n=3$ I think the answer should be $26/4$, while the answer in the answer book is $21/2$ (or $42/4$). I think the difference stems from how we treat the first $n$. In my understanding, the first number is a complete part and should be added to fraction, while the book treats it as part of fraction itself, thus multiplying it with $n^2+5$.

So, I just want to understand which convention is correct.

This is from problem 6 in exercise 9.1 on page 180 of the book *Sequences and Series*.

Here is the answer sheet from the book (answer 6, 3rd element):

- $3,8,15,24,35$
- $\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{5}{6}$
- $2, 4, 8, 16 \text{ and } 32$
- $-\dfrac{1}{6},\dfrac{1}{6},\dfrac{1}{2},\dfrac{5}{6},\dfrac{7}{6}$
- $25,-125,625,-3125,15625$
- $\dfrac{3}{2},\dfrac{9}{2},\dfrac{21}{2},21,\dfrac{75}{2}$
- $65, 93$
- $\dfrac{49}{128}$
- $729$
- $\dfrac{360}{23}$
- $3, 11, 35, 107, 323$; $3+11+35+107+323+…$
- $-1,\dfrac{-1}{2},\dfrac{-1}{6},\dfrac{-1}{24},\dfrac{-1}{120}$; $-1+(\dfrac{-1}{2})+(\dfrac{-1}{6})+(\dfrac{-1}{24})+(d\frac{-1}{120})+…$
- $2, 2, 1, 0, -1$; $2+2+1+0+(-1)+…$
- $1,2,\dfrac{3}{5},\dfrac{8}{5}$

## Best Answer

in elementary school math the fraction $x\frac{y}{z}$ usually means $x+\frac{y}{z}$ and is called a mixed fraction.

However these are almost never used after junior high.

Most of the time when you see $x\frac{y}{z}$ the two terms should be multiplied, so it is equal to $\frac{xy}{z}$.