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Show that P(n): 3^(n) is less than 15 is...

Show that P(n): `3^(n)` is less than 15 is true for `n ne 2`

Text Solution

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From P(n) `Rightarrow P(n+1)` we cannot say that P(n) is true for any. For the principleof mathematical induction it should have been give that `P(n) Rightarrow P(n+1)` and P(n) is true for some fixed +ve integer say n=m
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Knowledge Check

  • Let P(n) : 2^(n +2) lt 3 ^n , is true for

    A
    `n in N`
    B
    ` n gt n , AA n in N`
    C
    `n gt 2, AA n in N`
    D
    None of these

  • For all n in N, n^(4) is less than

    A
    `10^(n)`
    B
    `4^(n)`
    C
    4n
    D
    `10^(10)`

  • If (n)/(p) ratio is less than I, the nuclide can:

    A
    K-caputure
    B
    emits positron
    C
    emit `beta`-particle
    D
    emit `alpha`-particle