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

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

1. \lim_{x \to \infin} \frac{1}{x^2} = 0

This formula says that I can make the values of \frac{1}{x^2} as close as I would like to 0, so long as I make x sufficiently large.

2. \sum_{n = 0}^{\infin} 2^{-n} = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots  = 2

This formula says that you can make the sum \sum_{n=0}^{i} 2^{-n} as close as you would like to 2 by making i sufficiently large.