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Perhaps I am not seeing something but the example in my textbook on a chapter for mathematical induction asks to prove, for all $n\geq1$,
$$P(n):\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n(n+1)}=\frac{n}{n+1}$$ It explicitly states, $$P(1):\frac{1}{1.2}=\frac{1}{2}=\frac{1}{1+1}$$ Is true so we can proceed with further induction... but 1 over 1.2 is not the same as 0.5. And bluntly put, this is simply where I am stuck. I have never come across a question of this sort where the relation between numbers exists within itself, so to say. And I'm not quite sure whether there is a way to describe 'values' within the numbers such as the example above where the number in the tenths place is 1 more than that in the ones place.

So in short,

How do I interpret the $n(n+1)$ in the above equation?

For further clarity, I am currently interpreting it as multiplication as you would normally. I also do not know the name given to such a relation.

Doobius
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    The dots are meant to be read as multiplication. This is fairly common in some older textbooks. – Arbutus Jun 15 '21 at 18:34

1 Answers1

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Those are not decimals. They are multiplication dots that should be centered on their lines.

By coincidence, in their one explicit example $$ "1.2" = 1 \cdot 2 = 2 = 1 + 1. $$

David C. Ullrich
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Ethan Bolker
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