Pismeni zadaci

Zadatak 1980

Test: MPsIIIVAIV_342

 

S Izračunaj:

a) $$\lim \limits_{n \to +\infty }\left ( \frac{n+3}{n-3}+\frac{n-3}{n+3}-2\right )\cdot \frac{n^3-27}{5n-15}$$

b) $$\lim \limits_{n \to +\infty }\frac{1\cdot 1!+2\cdot 2!+\cdots +n\cdot n!}{(n+1)!}$$

Zadatak 1902

Test: MPsIIIVAIV_326

 

N Izračunaj:

a) $$\lim \limits_{n \to +\infty }\left ( \frac{1+2+3+\cdots +n}{3n+1} -\frac{n+1}{6}\right )$$

b) $$\lim \limits_{n \to +\infty }\frac{1-\frac{1}{3}+\frac{1}{3^2}-\cdots +(-1)^n\cdot \frac{1}{3^n}}{1+\frac{1}{2}+\frac{1}{2^2}+\cdots +\frac{1}{2^n}}$$

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