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CBSE Class 11-science Answered

Please solve question 33 in photo 
question image
Asked by Vidushi412 | 19 Mar, 2019, 09:31: AM
answered-by-expert Expert Answer
begin mathsize 12px style f left parenthesis x right parenthesis space equals space fraction numerator open parentheses x plus 1 close parentheses over denominator left parenthesis x minus 1 right parenthesis squared space left parenthesis x minus 2 right parenthesis end fraction space equals space open parentheses negative 1 half close parentheses space open parentheses space x plus 1 space close parentheses space open parentheses 1 space minus space x close parentheses to the power of negative 2 end exponent open parentheses 1 minus x over 2 close parentheses to the power of negative 1 end exponent space equals space open parentheses negative 1 half close parentheses space open parentheses space x plus 1 space close parentheses space g left parenthesis x right parenthesis w h e r e space g left parenthesis x right parenthesis space equals space open parentheses 1 space minus space x close parentheses to the power of negative 2 end exponent open parentheses 1 minus x over 2 close parentheses to the power of negative 1 end exponent space equals space open parentheses 1 plus 2 x plus 3 x squared plus 4 x cubed plus...... close parentheses open parentheses 1 plus x over 2 plus open parentheses x over 2 close parentheses squared space plus open parentheses x over 2 close parentheses cubed space plus space........ close parentheses T o space g e t space c o e f f i c i e n t space o f space x to the power of n space i n space f left parenthesis x right parenthesis comma space w e space g e t space c o e f f i c e n t s space space o f space x to the power of n minus 1 end exponent space space a n d space x to the power of n space space a n d space a d d space t o g e t h e r c o e f f i c i e n t space o f space x to the power of n minus 1 end exponent space i n space g left parenthesis x right parenthesis space colon space space n plus fraction numerator n minus 1 over denominator 2 end fraction space plus fraction numerator n minus 2 over denominator 4 end fraction space space plus space..........2 over 2 to the power of n minus 2 end exponent space plus 1 over 2 to the power of n minus 1 end exponent c o e f f i c i e n t space o f space x to the power of n space i n space g left parenthesis x right parenthesis space equals space left parenthesis n plus 1 right parenthesis space plus space n over 2 plus fraction numerator n minus 1 over denominator 4 end fraction space plus space........... plus space 3 over 2 to the power of n minus 2 end exponent plus 2 over 2 to the power of n minus 1 end exponent plus 1 over 2 to the power of n i f space w e space a d d space b o t h space c o e f f i c i e n t s space comma space w e space g e t space 2 n open square brackets 1 plus 1 half plus 1 fourth plus.......1 over 2 to the power of n minus 1 end exponent close square brackets space space minus open square brackets 1 half plus 2 over 4 plus 3 over 8 plus....... plus fraction numerator n minus 2 over denominator 2 to the power of n minus 2 end exponent end fraction plus fraction numerator n minus 1 over denominator 2 to the power of n minus 1 end exponent end fraction close square brackets minus open square brackets 1 fourth plus 2 over 8 plus.... plus space fraction numerator n minus 2 over denominator 2 to the power of n minus 1 end exponent end fraction close square brackets plus 1 plus 1 over 2 to the power of n equals space 2 n open square brackets 1 plus 1 half plus 1 fourth plus.......1 over 2 to the power of n minus 1 end exponent close square brackets space space minus 3 over 2 open square brackets 1 half plus 2 over 4 plus 3 over 8 plus....... plus fraction numerator n minus 2 over denominator 2 to the power of n minus 2 end exponent end fraction close square brackets plus 1 plus 1 over 2 to the power of n equals space 2 n open square brackets 1 plus 1 half plus 1 fourth plus.......1 over 2 to the power of n minus 1 end exponent close square brackets space space minus 3 over 4 open square brackets 1 plus 2 cross times open parentheses 1 half close parentheses plus 3 cross times open parentheses 1 half close parentheses squared plus....... plus open parentheses n minus 2 close parentheses cross times open parentheses 1 half close parentheses to the power of n minus 3 end exponent plus open parentheses n minus 1 close parentheses cross times open parentheses 1 half close parentheses to the power of n minus 2 end exponent close square brackets plus 1 space plus 1 over 2 to the power of n space............... left parenthesis 1 right parenthesis I n space t h e space a b o v e space e x p r e s s i o n space space left parenthesis 1 right parenthesis comma space space space space f i r s t space left square bracket space right square bracket space t e r m space i s space t h e space s u m space o f space g e o m e t r i c space p r o g r e s s i o n space t h a t space e q u a l s space space space 4 n open parentheses 1 space minus open parentheses 1 half close parentheses to the power of n close parentheses s e c o n d space left square bracket space right square bracket space t e r m space e q u a l s space 4 open square brackets space 1 space minus space open parentheses n plus 1 close parentheses open parentheses 1 half close parentheses to the power of n close square brackets space left curly bracket space t h i s space i s space o b t a i n e d space b y space d i f f e r e n t i a t i n g space fraction numerator 1 minus x to the power of n over denominator 1 minus x end fraction space right curly bracket B y space s i m p l i f y i n g space t h e space e x p r e s s i o n space left parenthesis 1 right parenthesis space b y space u sin g space t h e s e s space s u b s t i t u t i o n comma space w e space g e t space t h e space r e q u i r e d space c o e f f i c i e n t end style
Answered by Thiyagarajan K | 21 Mar, 2019, 09:03: AM

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