---
title: "Problem Set #1: Solutions"
author: "Milica Cudina"
date: "`r Sys.Date()`"
output: pdf_document
---
<!-- The author of this template is Dr. Gordan Zitkovic.-->
<!-- The code chunk below contains some settings that will  -->
<!-- make your R code look better in the output pdf file.  -->
<!-- If you are curious about what each option below does, -->
<!-- go to https://yihui.org/knitr/options/ -->
<!-- If not, feel free to disregard everything ...  -->
```{r echo=FALSE, warning=FALSE, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.align="center",
  fig.pos="t",
  strip.white = TRUE
)
```
<!-- ... down to here. -->

---

Create an `R`-notebook which prints out the answers to the following problems. All of your work and calculations **must** be done in `R`.

# Arithmetic (1 point each)
## Problem 1. 
Divide 792 by 11. 

*Solution:*
```{r}
792/11
```


## Problem 2. 
Find the square root of $\pi$

*Solution:*
```{r}
pi^(1/2)
sqrt(pi)
```

## Problem 3. 
Calculate $e^2$

*Solution:*
```{r}
exp(2)
```

## Problem 4. 
Find the fourth root of 256.

*Solution:*
```{r}
256^(1/4)
```


## Problem 5. 
Calculate the natural logarithm of 2.

*Solution:*
```{r}
log(2)
```


# Variables and vectors
## Problem 6. **(2 points)** 
Assign the value 3 to variable `a` and  the value 7 to variable `b`; print out their product

*Solution:*
```{r}
a=3
b=7
a*b
```

## Problem 7. **(3 points)** 
Set the vector `v` to be the numbers between -2 and 4 (inclusive); set the vector `w` to be the first 7 natural numbers; what do you get when you multiply `v` by `w`?

*Solution:*
```{r}
v=-2:4
w=1:7
v*w
```

# Loops
## Problem 8. **(5 points)**
Write and execute a chunk of code which calculates and prints out the sum of squares of the first $n$ natural numbers for $n=1, 2, \dots, 25$. 

*Solution:*
This the sum of squares of the first $10$ natural numbers
```{r}
sum((1:10)^2)
```

My full solution:
```{r}
for (n in 1:25){
  print(sum((1:n)^2))
}
```