CBSE Class 11-science Answered

$I f space t h e space c o e f f i c i e n t space o f space s e c o n d space comma space t h i r d space a n d space f o u r t h space t e r m s space i n space t h e space e x p a n s i o n space o f space left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space a r e space i n space A P thin space t h e n space f i n d space t h e space v a l u e space o f space 2 n squared minus 9 n plus 7 ?$ Please provide solution to this question

Asked by Topperlearning User | 08 Oct, 2016, 02:09: PM

Expert Answer

$C o e f f i c i e n t space o f space 2 n d space t e r m equals T subscript 2 equals C presuperscript 2 n end presuperscript subscript 1 C o e f f i c i e n t space o f space 3 r d space t e r m equals T subscript 3 equals C presuperscript 2 n end presuperscript subscript 2 C o e f f i c i e n t space o f space 4 t h space t e r m equals T subscript 4 equals C presuperscript 2 n end presuperscript subscript 3 T subscript 2 comma T subscript 3 comma T subscript 4 space end subscript space a r e space i n space A P space s o 2 T subscript 3 equals T subscript 2 plus T subscript 4 2 C presuperscript 2 n end presuperscript subscript 2 equals C presuperscript 2 n end presuperscript subscript 1 plus C presuperscript 2 n end presuperscript subscript 3 2 left parenthesis 2 n right parenthesis left parenthesis 2 n minus 1 right parenthesis divided by 2 equals 2 n plus fraction numerator 2 n left parenthesis 2 n minus 1 right parenthesis left parenthesis 2 n minus 2 right parenthesis over denominator 6 end fraction 2 n minus 1 equals 1 plus fraction numerator left parenthesis 2 n minus 1 right parenthesis left parenthesis 2 n minus 2 right parenthesis over denominator 6 end fraction 12 n minus 12 equals 4 n squared minus 6 n plus 2 4 n squared minus 18 n plus 14 equals 0 2 n squared minus 9 n plus 7 equals 0$