Wykaż że, jeżeli
: 26 sie 2007, o 14:44
Jeżeli \(\displaystyle{ \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=...=\frac{a_{n}}{b_{n}} b_{1}+b_{2}+...+b_{n}\neq0}\)
to
\(\displaystyle{ \frac{a_{1}+a_{2}+a_{3}+...+a_{n}}{b_{1}+b_{2}+b_{3}+...+b_{n}}=\frac{a_{1}}{b_{1}}}\)
Poprostu
\(\displaystyle{ \frac{a_{1}+a_{1}+a_{1}+a_{1}+...}{b_{1}+b_{1}+b_{1}+b_{1}+...}}\) skoro \(\displaystyle{ \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}}\)
to
\(\displaystyle{ \frac{a_{1}+a_{2}+a_{3}+...+a_{n}}{b_{1}+b_{2}+b_{3}+...+b_{n}}=\frac{a_{1}}{b_{1}}}\)
Poprostu
\(\displaystyle{ \frac{a_{1}+a_{1}+a_{1}+a_{1}+...}{b_{1}+b_{1}+b_{1}+b_{1}+...}}\) skoro \(\displaystyle{ \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}}\)