ધારો કે, ……..$a, ar, ar^2 , ar^3 …..ar^{48}, ar^{49}$ એ સમગુણોત્તર શ્રેણીમાં છે. 

$a_1 = a, a_2  = ar, a_3 = ar^2,…,a_{49} = ar^{48}, a_{50} = ar^{49}$ છે.

હવે, $\frac{{{a_1} – {a_3} + {a_5} – … + {a_{49}}}}{{{a_2} – {a_4} + {a_6} – … + {a_{50}}}}\,\,$

${\text{ =  a  –  a}}{{\text{r}}^{\text{2}}}{\text{  +  a}}{{\text{r}}^{\text{4}}}{\text{  – ….. }}$.(25 પદ સુધી) $/$${\text{ar  –  a}}{{\text{r}}^{\text{3}}}{\text{  +  a}}{{\text{r}}^{\text{5}}}{\text{  – …….. }}{\text{.}}$(25 પદ સુધી)

$ = \frac{{\frac{{a[1 – {{( – {r^2})}^{25}}]}}{{1 – {{( – r)}^2}}}}}{{\frac{{ar[1 – {{( – {r^2})}^{25}}]}}{{1 – {{( – r)}^2}}}}}\,\,\, = \frac{a}{{ar}} = \frac{{{a_1}}}{{{a_2}}}$