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Find the greater number between 100^(100...

Find the greater number between `100^(100) ` and (300)!.

Text Solution

Verified by Experts

Using Result (ii) , We know that `((n)/(3))^(n) lt n! `
Putting n = 300 , we get
`(100)^(300) lt (300) !` …(i)
But ` (100)^(100) lt (100)^(300)` …(ii)
From Eqs. (i) and (ii) , we get
`(100)^(100) lt (100)^(300) lt (300) ! `
` rArr (100)^(100) lt (300) !`
Hence , the greater number is (300)!.
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