Question

Va rog ajutor.
imaginea de mai sus. nr1
lim din n->infinit
$(1 \div ( {n}^{2} + 1)) + (1 \div ({n}^{2} + 2)) + ..... + (1 \div ({n}^{2} + n))$
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Answer 1

Răspuns:

$\lim _{n\to \infty }\left(\frac{1}{\sqrt{n^2}+1}+\frac{1}{\sqrt{n\:^2+2}}+...+\frac{1}{\sqrt{n\:^2+n}}\right)=0$

Explicație pas cu pas:

$\lim _{n\to \infty }\left(\frac{1}{\sqrt{n^2}+1}+\frac{1}{\sqrt{n\:^2+2}}+...+\frac{1}{\sqrt{n\:^2+n}}\right)\\\\\lim _{n\to \infty }\left(\frac{1}{\sqrt{\infty ^2}+1}+\frac{1}{\sqrt{\infty \:^2+2}}+...+\frac{1}{\sqrt{\infty \:^2+\infty }}\right)$

atunci cand numitorul unei fractii contine simbolul ∞, atunci fractia este egala cu 0 .

$\lim _{n\to \infty }(0+0+...+0)\\\lim _{n\to \infty }\left(\frac{1}{\sqrt{n^2}+1}+\frac{1}{\sqrt{n\:^2+2}}+...+\frac{1}{\sqrt{n\:^2+n}}\right)=0$

Succes! :)