Parentheses
You may not just calculate something in parentheses first.
Example 1
We start with the formula
where we suspect that this will bring 1 for n→∞, as
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However, that is wrong. Infinity is not a number (it has no fixed value), and you should always be careful with the number 0. Let us therefore calculate more carefully. We use the binomial development and then get as the first two terms
All further terms are also positive numbers and so will just add more value. Therefore, we write
This gives
and that is already double our first result. What's going on here? We have not calculated in a proper way in the beginning. You may not only calculate a part of a calculation where infinite is used. So you may not just calculate something in parentheses first.