Question

Al doilea ex vă rog!! Raspunsul este 0

Answer 1

Răspuns:

$x_n=-1+\displaystyle\sum_{k=1}^n\left(\frac{k}{k!}-\frac{1}{k!}\right)=-1+\sum_{k=1}^n}\frac{1}{(k-1)!}-\sum_{k=1}^n}\frac{1}{k!}=\\=-1+1+\frac{1}{1!}+\frac{1}{2!}+\ldots+\frac{1}{(n-1)!}-\frac{1}{1!}-\frac{1}{2!}-\ldots-\frac{1}{n!}=-\frac{1}{n!}$

$\displaystyle\lim_{n\to\infty}x_n=0$

Explicație pas cu pas: