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summed numerator and summed denominator
If are any real fractions with positive denominators and
are the least and the greatest of the fractions, then
| (1) |
The equality signs are valid if and only if all fractions are equal; in this case one has
Proof. Set , …, . Then we have , which apparently has the lower bound and the upper bound . Dividing the three last expressions by the sum yields the asserted double inequality (1).
Related:
InequalityForRealNumbers
Major Section:
Reference
Type of Math Object:
Theorem
Parent:
Mathematics Subject Classification
11A99 None of the above, but in MSC2010 section 11Axx- Forums
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new correction: Typo by suitangi
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new question: Creating another set with same cardinality. by hkkass
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new image: ProblemOneRevised by unlord
new Education: Chapter II by rspuzio
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new collection: The Calculus by Davis and Brenke by rspuzio
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Contains own proof by rm50 ✓


