Matematyka.pl

mam do policzenia \(\displaystyle{ i_{14}^{j}}\)
Dane sa liczby poszczegolnych zebow kol zebatych.

Obliczenia:
\(\displaystyle{ i_{1j}^3=1-i_{13}^j}\)
\(\displaystyle{ i_{13}^{j} =\frac{-z_{2}}{z_{1}}\cdot \frac {z_3}{z_2}}\)
a wiec:
\(\displaystyle{ i_{1j}^3=1-i_{13}^j=1-\frac{-z_{2}}{z_{1}}\cdot \frac {z_3}{z_2}=1 +\frac{z_3}{z_1}=\frac {z_3+z_1}{z_1}}\)

teraz licze \(\displaystyle{ i_{j4}^3}\)
\(\displaystyle{ i_{j4}^3=\frac{1}{i_{4j}^3}}\)
\(\displaystyle{ i_{4j}^3 = 1- i_{43}^j=1-\frac{z_{2'}}{z_4}\cdot \frac{z_3}{z_2}= \frac{z_4 z_2-z_{2'}z_3}{z_4 z_2}}\)
wiec:
\(\displaystyle{ i_{j4}^3= \frac{z_4 z_2}{z_4 z_2-z_{2'}z_3}}\)
Ostatecznie:

\(\displaystyle{ i_{14}^3= i_{1j}^3 \cdot i_{j4}^3 = \frac {z_3+z_1}{z_1} \cdot \frac{z_4 z_2}{z_4 z_2-z_{2'}z_3}}\)
Prosze o ocene moich obliczen, jezeli to mozliwe . Pozdrawiam.