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A chruthú leis an ionduchtú go bhfuil n! > 2 n , n > 3, n  N

A chruthú leis an ionduchtú go bhfuil n! > 2 n , n > 3, n  N. Cruthaigh: n! > 2 n for n = 4 n! = 4! = 24 2 4 = 16 24 > 16 Fíor do n = 4. Glac leis gur fíor é i gcás n = k Dá bhrí sin k ! > 2 k Cruthaigh go bhfuil sé fíor i gcás n = k + 1.

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A chruthú leis an ionduchtú go bhfuil n! > 2 n , n > 3, n  N

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  1. A chruthú leis an ionduchtú go bhfuil n! > 2n, n > 3, n  N Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

  2. Cruthaigh:n! > 2n for n = 4 n! = 4! = 24 24 = 16 24 > 16 Fíor do n = 4 Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

  3. Glac leis gur fíor é i gcás n = k • Dá bhrí sin k! > 2k • Cruthaigh go bhfuil sé fíor i gcás n = k + 1 Iolraigh an Dá Thaobh faoi k + 1 (k + 1)k! > (k + 1)2k (k + 1)! >(k + 1)2k ((k+1)k!=(k+1)!) • (k + 1)! > 2k + 1(k + 1 > 2 k > 3) Má tá sé fíor i gcás n = k, tugann sé sin le fios gur fíor é i gcás n = k + 1 tá sé fíor do n = 4. Dá réir sin k! > 2k nuair a bhionn n > 3, n  N Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

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