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Power by using the principle of Mathematical Induction that `n!>= 2^(n-1)` for every...
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`n! >= 2^(n-1) `
`n = 1`
`LHS = 1! =1`
`RHS = 2^(1-1) = 1`
`LHS = RHS`
For `n = 1` result is true.
Let us assume that for n = p where `p>=1` and a positive integer the result is true.
`n = p+1`
`p!>=2^(p-1)` multiply both sides by `(p+1` ).
`p>=1` therefore `(p+1)>=2`
`(p+1)!>= 2^(p-1)xx2` is valid
So for n = p+1 the result is true.
So from mathematical induction it is proved that `n! >= 2^(n-1) `
Posted by jeew-m on September 16, 2013 at 4:15 AM (Answer #1)
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