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is an increasing sequence
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(Theorem)
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Proof. To see this, rewrite
 and divide two consecutive terms of the sequence:
Since
, we have
hence the sequence is increasing. 
Proof. By an inequality for differences of powers, we have
From this we may conclude
The last line follows from the factorization
 . Dividing through,
which simplifies to
or

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" is an increasing sequence" is owned by rspuzio.
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(view preamble)
Cross-references: line, powers, differences, inequality, decreasing, terms, consecutive, divide, increasing, sequence
This is version 6 of is an increasing sequence, born on 2006-03-25, modified 2007-05-16.
Object id is 7775, canonical name is 11nnIsAnIncreasingSequence.
Accessed 6649 times total.
Classification:
| AMS MSC: | 33B99 (Special functions :: Elementary classical functions :: Miscellaneous) |
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Pending Errata and Addenda
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