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Astronamus
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I am deleting
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daster said:This is kind of related, is:
[tex]\sum_{r=1}^{n} r![/tex]
ever a perfect square? I know this is true for n=1 and n=3, but what about in general?
I'd like hints only, please.
Wow... That's brilliant.matt grime said:just work out the squares of the residues mod 10, which is waht i meant by considering a suitable mod thing
and if 3 divides N and N is a square then 9 divides N is what I meant
daster said:...but I really didn't know that if a number ends in 3 it's a perfect square.
Yes, sorry, that's what I meant.Rogerio said:And it is not!
As I had said, if a number ends in 3, it is not a perfect square.
To prove that 1/2 + 2/3 + 3/4 does not equal a whole number, we can use the concept of common denominators. When we add fractions, we need to have a common denominator. In this case, the common denominator is 12. However, when we add the fractions, we get a result of 11/12, which is not a whole number.
Yes, we can provide a mathematical explanation for why 1/2 + 2/3 + 3/4 does not equal a whole number. As mentioned before, the common denominator for these fractions is 12. When we add them, we get a result of 11/12, which is not a whole number. In other words, the sum of the fractions is less than 1, which means it is not a whole number.
Yes, there is a simpler way to explain why 1/2 + 2/3 + 3/4 does not equal a whole number. We can think of fractions as parts of a whole. In this case, the fractions represent parts of a whole divided into 12 equal parts. When we add them, we get a result that is less than 12, which means it is not a whole number.
Yes, we can provide an example to demonstrate why 1/2 + 2/3 + 3/4 does not equal a whole number. Let's say we have a pizza divided into 12 equal slices. If we take 6 slices (1/2 of the pizza), 8 slices (2/3 of the pizza), and 9 slices (3/4 of the pizza), we will have a total of 23 slices, which is more than the 12 slices that make up the whole pizza. This shows that the sum of the fractions is not equal to a whole number.
The significance of proving that 1/2 + 2/3 + 3/4 does not equal a whole number is that it highlights the importance of understanding fractions and how they relate to whole numbers. It also emphasizes the need for a common denominator when adding fractions. This proof can also be applied to other fractions and serves as a reminder to always double-check our calculations to ensure they are accurate.