help on induction! (1 Viewer)

AreYouAlright?

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Personally, i'd leave it and move on and hope no one else in the state can do it. However, my tactics don't always work out :D
 

Pace_T

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can someone please explain the first two parts i don't get them
thanks.
 

rama_v

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Pace_T said:
can someone please explain the first two parts i don't get them
thanks.

(1) prove for n=6
ln 6! > 6
6.57>6
true

(2) assueme n=k
ln n! - k >0

(3) prove true for n=k+1
i.e. prove ln(k+1)!>k+1

LHS = ln(k+1)!
= lnk! +ln(k+1)

but ln k! + ln(k+1) > ln(k+1) +k
for k>6, k+1 >e
ln (k+1) > ln e since ln e = 1
.: ln[(k+1)!]>1+k

Hence if the result is true for n=k it has been proven true for n=k+1, so it is true for all n where n>6, proven by mathematical induction...

Full solutions: http://www.boredofstudies.org/cours...matics_Extension_1_T_Trial_Solutions_CSSA.pdf


so therefore ln n! >k for all positve integers n>6 proven true by mathematical induction

For the second part:
ln n! > n
eln n! > en
1/eln n! < 1/en
so 1/n! < 1/en
 
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