question_answer

If \[\frac{1+i}{1+{{2}^{2}}i}\times \frac{1+{{3}^{2}}}{1+{{4}^{2}}i}\times ..\times \frac{1+{{(2n-1)}^{2}}i}{1+{{(2n)}^{2}}i}=\frac{a+ib}{C+id},\] then \[\frac{2}{17}\times \frac{82}{257}\times ...\times \frac{1+(2n-1)}{1+{{(2n)}^{4}}}=\]

A)  \[\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}\]   

B)  \[\frac{{{a}^{2}}}{{{c}^{2}}}+\frac{{{b}^{2}}}{{{d}^{2}}}\]

C)  \[\frac{{{a}^{2}}}{{{c}^{2}}}+\frac{{{b}^{2}}}{{{d}^{2}}}\]    

D)  None of these