# pifinity's problem set

## Finalized Problems

#### Problem I

Evaluate $\frac{48}{32} + \frac{24}{16}.$

#### Solution I

Simplify; no denominator conversion needed: $$\frac{48}{32} + \frac{24}{16}=\frac{3}{2} + \frac{3}{2} = \boxed{3}.$$

## Unconfirmed Problems

#### Problem

What is the $\,?\,"$ term? $$(100-96)+100+(96-92)+94+(92-88)+88+\hdots+?+(4-0)$$

#### Solution

We first wish to find the number of "telescoping" terms. The first one is $100$ minus something, so we can label it $\tfrac{100}4=25.$ The last term is $4$ minus something, so we can label it $\tfrac{4}4=1.$ Thus there are $25-(4-1)=22$ terms. Therefore, there are 21 gaps between the terms in parentheses. Since there is one less of the terms not in parentheses, then there are 20 gaps between these terms in total. And since $6$ is subtracted each time for the terms not in parentheses, then we have to subtract $6\times20=120$ from $100$: $$100-120=\boxed{-20}.$$

## Unsolved Problems

No Unsolved Problems.

This page has 12 official edits. The last edit was on 12:09, May 18, 2018.