perplexus.info :: Just Math : Factorialroot Fruition

Factorialroot Fruition (Posted on 2022-11-24)

Let us consider:

X= ⁹⁹√(99!), and:

Y= ¹⁰⁰√(100!)

Determine, without direct evaluation and using analytic/semi-analytic (simple calculator + p&p) techniques, which of these is greater:

• (i) X or Y

• (ii) X/99 or Y/100

*** Computer programs/excel solver/advanced calculators/online solvers can be used only for purposes of verification.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(i) Y is greater than X.
(ii) X/99 is greater than Y/100.
For an explanation, refer to the solution posted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Brian Smith	2022-11-24 13:55:49
Solution by analogy	Steve Herman	2022-11-24 08:02:05

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