Potrebna mi je pomoc oko granicne vrednosti ovog niza. Zadatak glasi ovako :
[dispmath]\lim_{n\to\infty}\left(\frac{3}{4}+\frac{5}{16}+\frac{9}{64}+\cdots+\frac{1+2^n}{4^n}\right)[/dispmath]
Index stranica ‹ MATEMATIČKA ANALIZA ‹ LIMESI
Limes niza
Pregled za štampanje • Pregled za štampanje svih postova u temi • 3 Posta
• Stranica 1 od 1
Limes niza
od pele123 » Četvrtak, 15. Decembar 2016, 16:23
- Postovi: 6
- Zahvalio se: 6 puta
- Pohvaljen: 0 puta
Re: Limes niza
od mala_mu » Četvrtak, 15. Decembar 2016, 17:12
Ako uočiš da [inlmath]\frac{1+2^n}{4^n}[/inlmath] možeš napisati kao [inlmath]\left(\frac{1}{4}\right)^n+\left(\frac{1}{2}\right)^n[/inlmath], raspisujući tako svaki sabirak u nizu lako se vidi da se može iskoristiti:
[dispmath]1+q^2+q^3+\cdots+q^n=\frac{1-q^{n+1}}{1-q}[/dispmath] Naravno još trebaš dodati dvije [inlmath]1[/inlmath], i oduzeti ih, da možeš iskoristiti datu formulu.
Koliko vidim rješenje bi trebalo biti [inlmath]\frac{4}{3}[/inlmath]
[dispmath]1+q^2+q^3+\cdots+q^n=\frac{1-q^{n+1}}{1-q}[/dispmath] Naravno još trebaš dodati dvije [inlmath]1[/inlmath], i oduzeti ih, da možeš iskoristiti datu formulu.
Koliko vidim rješenje bi trebalo biti [inlmath]\frac{4}{3}[/inlmath]
Sorry I'm late a black cat blocked my path so I had to take a different way then a dragon came down and blocked my path then I saw an old lady having trouble crossing the street so I helped her then a cat was stuck in a tree and the owners asked me to help then I got lost on the road of life
Re: Limes niza
od mala_mu » Četvrtak, 15. Decembar 2016, 18:20
Uočih grešku u mom postu, treba:
[dispmath]1+{\color{red}q}+q^2+q^3+\cdots+q^n=\frac{1-q^{n+1}}{1-q}[/dispmath]
[dispmath]1+{\color{red}q}+q^2+q^3+\cdots+q^n=\frac{1-q^{n+1}}{1-q}[/dispmath]
Sorry I'm late a black cat blocked my path so I had to take a different way then a dragon came down and blocked my path then I saw an old lady having trouble crossing the street so I helped her then a cat was stuck in a tree and the owners asked me to help then I got lost on the road of life
3 Posta
• Stranica 1 od 1
Ko je OnLine
Korisnici koji su trenutno na forumu: Nema registrovanih korisnika i 7 gostiju