T h e space 7 to the power of t h end exponent space t e r m space f r o m space t h e space b e g i n n i n g space a n d space e n d space i n space t h e space e x p a n s i o n space o f open parentheses 2 to the power of 1 third end exponent plus 1 over 3 to the power of begin display style 1 third end style end exponent close parentheses to the power of n space a r e space e q u a l.
F i n d space t h e space v a l u e space o f space n.

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Asked by Topperlearning User | 8th Oct, 2016, 02:44: PM

Expert Answer:

T subscript 7 equals C presuperscript n subscript 6 open parentheses 2 close parentheses to the power of 6 over 3 end exponent open parentheses 1 third close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent
7 to the power of t h space end exponent t e r m space f r o m space t h e space e n d space i s space n minus 7 plus 2 equals left parenthesis to the power of blank n minus 5 right parenthesis to the power of t h end exponent space t e r m space f r o m space t h e space b e g i n n i n g.
T subscript n minus 5 end subscript equals C presuperscript n subscript n minus 6 end subscript open parentheses 2 close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent open parentheses 1 third close parentheses to the power of 6 over 3 end exponent
T subscript 7 equals T subscript n minus 5 end subscript
C presuperscript n subscript 6 open parentheses 2 close parentheses to the power of 6 over 3 end exponent open parentheses 1 third close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent equals C presuperscript n subscript n minus 6 end subscript open parentheses 2 close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent open parentheses 1 third close parentheses to the power of 6 over 3 end exponent
n o w space space C presuperscript n subscript 6 equals C presuperscript n subscript n minus 6 end subscript
s o space w e space g e t
2 squared open parentheses 1 third close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent equals open parentheses 2 close parentheses to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent open parentheses 1 third close parentheses squared
36 equals 6 to the power of fraction numerator n minus 6 over denominator 3 end fraction end exponent
fraction numerator n minus 6 over denominator 3 end fraction equals 2 rightwards double arrow n equals 12

Answered by  | 8th Oct, 2016, 04:44: PM

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