Dokazati da nejednakost:
![](https://static.elitesecurity.org/tex/f754a23c21b249bb3f0394be526e8af6.png)
vrijedi za svaki prirodan broj
![](https://static.elitesecurity.org/tex/88939dd08fc6bc15d767220e11a51c74.png)
Dokaz. Za
![](https://static.elitesecurity.org/tex/3571999c46e8761f6595934427c20dcd.png)
![](https://static.elitesecurity.org/tex/eec31ac409d04923c166fb1a5a8fb91c.png)
Za
![](https://static.elitesecurity.org/tex/ad4dd664172b6d6bb2c3128253ab776c.png)
![](https://static.elitesecurity.org/tex/24fd2e2194fee728f02922992f33e55a.png)
Pretpostavimo da nejednakost (*) vrijedi za
![](https://static.elitesecurity.org/tex/53fafa135597b42e28a9f4a87f196b6c.png)
![](https://static.elitesecurity.org/tex/8fe36547c6fe17a078f7ce212f76741f.png)
Ako dokažemo da relacija (*) vrijedi za
![](https://static.elitesecurity.org/tex/45b1723ca5ced6038d8a32477daf6c7a.png)
![](https://static.elitesecurity.org/tex/bd2b320696c94ea17dd122cd137b965c.png)
![](https://static.elitesecurity.org/tex/78a50d8a3bd1a15a271eab5577aa36d2.png)
![](https://static.elitesecurity.org/tex/cb293cd5fb40ce9f7e7c743b15ae0dc0.png)
Prema tome, ako je
![](https://static.elitesecurity.org/tex/ee92a169012e1ba60740cc7c1b59d34e.png)
![](https://static.elitesecurity.org/tex/ec393c01358ad3a07d1fae39aeab736d.png)
Napomena: Dokaz smo mogli i ovako provesti:
1)Za
![](https://static.elitesecurity.org/tex/3571999c46e8761f6595934427c20dcd.png)
![](https://static.elitesecurity.org/tex/8a8337746c11ea37cc1bc0cc749bebc0.png)
2)Pretpostavimo da je za
![](https://static.elitesecurity.org/tex/ce6f4b6b1393824eee12d717925d27bf.png)
![](https://static.elitesecurity.org/tex/c874af37137ab3185c2c35b59824632e.png)
Dokažimo valjanost tvrdnje i za
![](https://static.elitesecurity.org/tex/13a81830b510c947a0938efee58ba530.png)
![](https://static.elitesecurity.org/tex/8075b5053c1d5a70e8973f645ed5ce16.png)
Zaista,
![](https://static.elitesecurity.org/tex/3e578f088afbfc4cb1acd663f444dbe8.png)
![](https://static.elitesecurity.org/tex/a25bbef7df1ebeac28ac7ab49233b0c3.png)
Ovim je dokaz završen.
Kraj citata.
Meni nije jasno odkuda ovo što sam označio plavom bojom. Je li u pitanju neka krupna štamparska greška ili je meni nešto promaklo? Ako je ovo označeno plavom bojom nepravilno, kako treba pravilno?
[Ovu poruku je menjao R A V E N dana 26.10.2013. u 13:22 GMT+1]