1 / 3

A chruthú leis an ionduchtú go bhfuil 2 n ≥ n 2 for n ≥ 4, n  N

A chruthú leis an ionduchtú go bhfuil 2 n ≥ n 2 for n ≥ 4, n  N. A chruthú leis an ionduchtú go bhfuil 2 n ≥ n 2 for n ≥ 4, n  N. Cruthaigh go bhfuil sé fíor i gcás n = 4 2 n ≥ n 2 2 n = 2 4 = 16 n 2 = 4 2 = 16 16 ≥ 16 Dá bhrí sin tá sé fíor do n = 4.

keaton-knox
Download Presentation

A chruthú leis an ionduchtú go bhfuil 2 n ≥ n 2 for n ≥ 4, n  N

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A chruthú leis an ionduchtú go bhfuil 2n ≥ n2 for n ≥ 4, n  N Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

  2. A chruthú leis an ionduchtú go bhfuil 2n ≥ n2 for n ≥ 4, n  N Cruthaigh go bhfuil sé fíor i gcás n = 4 2n ≥ n2 2n = 24 = 16 n2 = 42 = 16 16 ≥ 16 Dá bhrí sin tá sé fíor do n = 4. Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

  3. Glac leis gur fíor é i gcás n = k Dá bhrí sin 2k ≥ k2 Cruthaigh go bhfuil sé fíor i gcás n = k + 1 Iolraigh an Dá Thaobh faoi 2 2.2k ≥ 2k2 2k + 1 ≥ k2 + k2 (Mar tá k ≥ 4 agus k N dá bhrí sin k2>2k + 1.) Dá bhrí sin2k +1 ≥ k2 + 2k + 1 Dá réir sin 2k +1≥ (k + 1)2 Má tá sé fíor i gcás n = k, tugann sé sin le fios gur fíor é i gcás n = k + 1 Is fíor é i gcás n = 1. Dá réir sin leis an Ionduchtú (1 + x)n ≥1+nx, n ≥ 4, n N. Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

More Related