I f space A equals left parenthesis 1 space plus space r to the power of a space plus space r to the power of 2 a end exponent space plus...... infinity right parenthesis space a n d space B equals left parenthesis 1 space plus space r to the power of b space plus space r to the power of 2 b end exponent space plus....... infinity right parenthesis comma t h e n space p r o v e space t h a t : r equals open parentheses fraction numerator A minus 1 over denominator A end fraction close parentheses to the power of 1 over a end exponent space equals space open parentheses fraction numerator B minus 1 over denominator B end fraction close parentheses to the power of 1 over b end exponent

Asked by Olivia Adhikary | 19th Aug, 2014, 11:26: AM

Expert Answer:

F r o m space g i v e n space i n f o r m a t i o n space w e space c a n space g e t A equals fraction numerator 1 over denominator 1 minus r to the power of a end fraction comma space B equals fraction numerator 1 over denominator 1 minus r to the power of b end fraction R e w r i t i n g space e x p r e s s i o n space g i v e s 1 minus r to the power of b equals 1 over A r to the power of b equals 1 minus 1 over A r equals open parentheses fraction numerator A minus 1 over denominator A end fraction close parentheses to the power of 1 over a end exponent  S i m i l a r l y space f o r space B space a l s o space w e space g e t space r equals open parentheses fraction numerator B minus 1 over denominator B end fraction close parentheses to the power of 1 over b end exponent

Answered by Dharma Teja | 19th Aug, 2014, 03:57: PM

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