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Home / Doubts and Solutions/JEE/Mathematics

ques 35

Asked by chandanbr6004 11th November 2017, 12:33 AM
Answered by Expert
Answer:
begin mathsize 16px style space sum from r equals 1 to n of open parentheses a r plus b close parentheses alpha to the power of r minus 1 end exponent equals a left parenthesis 1 plus 2 alpha plus 3 alpha squared plus midline horizontal ellipsis plus n alpha to the power of n minus 1 end exponent right parenthesis space plus b left parenthesis 1 plus alpha plus alpha squared plus midline horizontal ellipsis plus alpha to the power of n minus 1 end exponent right parenthesis..... left parenthesis 1 right parenthesis 1 plus 2 alpha plus 3 alpha squared plus midline horizontal ellipsis plus n alpha to the power of n minus 1 end exponent space t h i s space i s space A G P 1 plus alpha plus alpha squared plus midline horizontal ellipsis plus alpha to the power of n minus 1 end exponent space t h i s space i s space G P s u m space o f space G P space equals fraction numerator 1 minus alpha to the power of n over denominator 1 minus alpha end fraction S u m space o f space A G P equals fraction numerator 1 over denominator 1 minus alpha end fraction plus fraction numerator alpha minus alpha to the power of n over denominator left parenthesis 1 minus alpha right parenthesis squared end fraction minus fraction numerator n alpha to the power of n over denominator 1 minus alpha end fraction left parenthesis m e t h o d space o f space f i n d i n g space s u m space o f space A G P space left parenthesis S minus r S space semicolon space r space c o m m o n space r a t i o right parenthesis right parenthesis S u b space i n space left parenthesis 1 right parenthesis w e space g e t a open parentheses fraction numerator 1 over denominator 1 minus alpha end fraction plus fraction numerator alpha minus alpha to the power of n over denominator left parenthesis 1 minus alpha right parenthesis squared end fraction minus fraction numerator n alpha to the power of n over denominator 1 minus alpha end fraction close parentheses space plus b open parentheses fraction numerator 1 minus alpha to the power of n over denominator 1 minus alpha end fraction close parentheses..... left parenthesis 2 right parenthesis n o w space alpha equals cos fraction numerator 2 straight pi over denominator n end fraction plus i sin fraction numerator 2 straight pi over denominator n end fraction alpha to the power of n equals cos 2 straight pi plus i sin 2 straight pi space equals space 1 space Sub space in space.... left parenthesis 2 right parenthesis fraction numerator negative na over denominator 1 minus straight alpha end fraction....................... option space no.1 end style
Answered by Expert 7th December 2017, 12:30 PM
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Tags: geometric-progressions special-sequences-and-series complex-numbers
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