Question

c) aratati ca 1/N - 1/n+m = m/ n* (n+m), pentru orice neN

Answer 1

[tex]\frac{1}{n}-\frac{1}{n+m}=\frac{m}{n\cdot (n+m)} [/tex]

$\Leftrightarrow \frac{n+m}{n\cdot(n+m)}-\frac{n}{n\cdot n(n+m)}=\frac{m}{n\cdot(n+m)}\\ \\ \Leftrightarrow \frac{n+m-n}{n\cdot (n+m)}=\frac{m}{n\cdot (n+m)}\\ \\ \Leftrightarrow \frac{m}{n\cdot (n+m)}=\frac{m}{n\cdot (n+m)} \ (Adevarat)$