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CBSE Class 11-science Answered

T h r e e space c o n s e c u t i v e space c o e f f i c i e n t s space i n space t h e space e x p a n s i o n space left parenthesis 1 plus x right parenthesis to the power of n space b e space 165 comma space 330 space a n d space 462 comma space f i n d space n space a n d space t h e space p o s i t i o n space o f space t h e space c o e f f i c i e n t s.
Asked by surajsubedi14 | 03 Mar, 2015, 10:20: AM
answered-by-expert Expert Answer
L e t space t h e space c o n s e c u t i v e space t e r m s space b e space left parenthesis r minus 1 right parenthesis comma r space a n d space left parenthesis r plus 1 right parenthesis fraction numerator C presuperscript n subscript r minus 1 end subscript over denominator C presuperscript n subscript r end fraction equals 165 over 330 rightwards double arrow fraction numerator begin display style fraction numerator n factorial over denominator left parenthesis n minus r plus 1 right parenthesis factorial left parenthesis r minus 1 right parenthesis factorial end fraction end style over denominator fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial r factorial end fraction end fraction equals 1 half space rightwards double arrow fraction numerator r over denominator n minus r plus 1 end fraction equals 1 half space left square bracket S i m p l i f y i n g space w e space g e t comma right square bracket..... left parenthesis i right parenthesis A l s o comma space fraction numerator C presuperscript n subscript r over denominator C presuperscript n subscript r plus 1 end subscript end fraction equals 330 over 462 rightwards double arrow fraction numerator begin display style fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial r factorial end fraction end style over denominator fraction numerator n factorial over denominator left parenthesis n minus r minus 1 right parenthesis factorial left parenthesis r plus 1 right parenthesis factorial end fraction end fraction equals 5 over 7 space rightwards double arrow fraction numerator r plus 1 over denominator n minus r end fraction equals 1 half left square bracket S i m p l i f y i n g space w e space g e t comma right square bracket....... left parenthesis i i right parenthesis S o l v i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t n equals 11 space a n d space r equals 4 T h e r e f o r e space t h e space p o s i t i o n space o f space t h e space c o e f f i c i e n t s space a r e space 3 r d comma space 4 t h space a n d space 5 t h.
Answered by Prasenjit Paul | 03 Mar, 2015, 12:00: PM

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