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Jonask

  • 3 years ago

show by induction that

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  1. Jonask
    • 3 years ago
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    \[n!<n^n\]

  2. shubhamsrg
    • 3 years ago
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    assuming k! < k^k .....(1) we have to prove (k+1)! < (k+1)^(k+1) (k+1)(k!) <(k + 1)^k * (k+1) since k+1 >0 we see k! < (k+1)^k ...(2) binomial expansion will show RHS = k^k + something positive from (1) , we easily see (2) is true..

  3. shubhamsrg
    • 3 years ago
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    hope you didnt mind i missed the initial step of induction..

  4. Jonask
    • 3 years ago
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    no i dont mind cos i had already done that ,it is great

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