Question

$25 \frac{41}{?}$
Please tell me ​

Answer 1

Answer:

Assuming you mean the average as the arithmetic mean of all integers from 25 to 41.

The average would be (well, you can ignore the integers between 25 and 41 exclusive) 25+412=3325+412=33

Actually, you would get the “same” answer for “any” evenly spaced domain that’s a subset of the real numbers D⊂RD⊂R . Try it with spaces of 1/n near 0.

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Another famous average is the geometric mean, called for being first constructed by early geometry but actually used in financials. The average would be (you can’t ignore the integers now) around 32.63, slightly less than 33, our first average, well it should always be small by the Arithmetic-Geometric Mean Inequality

However, you won’t get the “same” answer for “any” evenly spaced domain that’s a subset of the real numbers D⊂RD⊂R with the geometric mean. Trying to calculate with spaces of 1/n near 0 probably will be a bit impossible unless you knew a trick. (Spoiler Alert: The value from 1 and 2 is 4e4e , but the reason is for another day. - You try and observe for 25 to 41)