# Calculus/Infinite Limits/Infinity is not a number/Solutions

Write out an explanatory paragraph for the following limits that include ${\displaystyle \infty }$. Remember that you will have to change any comparison of magnitude between a real number and ${\displaystyle \infty }$ to a different phrase. In the second case, you will have to work out for yourself what the formula means.

1. ${\displaystyle \lim _{x\to \infty }{\frac {1}{x^{2}}}=0}$
This formula says that I can make the values of ${\displaystyle {\frac {1}{x^{2}}}}$ as close as I would like to 0, so long as I make x sufficiently large.
This formula says that I can make the values of ${\displaystyle {\frac {1}{x^{2}}}}$ as close as I would like to 0, so long as I make x sufficiently large.
2. ${\displaystyle \sum _{n=0}^{\infty }2^{-n}=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+\cdots =2}$
This formula says that you can make the sum ${\displaystyle \sum _{n=0}^{i}2^{-n}}$ as close as you would like to 2 by making ${\displaystyle i}$ sufficiently large.
This formula says that you can make the sum ${\displaystyle \sum _{n=0}^{i}2^{-n}}$ as close as you would like to 2 by making ${\displaystyle i}$ sufficiently large.