CBSE Class 11-science Answered

$F i n d space t h e space v a l u e space o f space C presuperscript n subscript 0 plus C presuperscript n subscript 2 plus C presuperscript n subscript 4 plus... ?$ Please provide solution to this question

Asked by Topperlearning User | 08 Oct, 2016, 01:56: PM

Expert Answer

$left parenthesis 1 plus x right parenthesis to the power of n equals C presuperscript n subscript 0 plus C presuperscript n subscript 1 x plus C presuperscript n subscript 2 x squared plus.... f o r space x equals 1 space w e space h a v e left parenthesis 2 right parenthesis to the power of n equals C presuperscript n subscript 0 plus C presuperscript n subscript 1 plus C presuperscript n subscript 2 plus.... rightwards arrow circle enclose 1 f o r space x equals negative 1 space w e space h a v e 0 equals C presuperscript n subscript 0 minus C presuperscript n subscript 1 plus C presuperscript n subscript 2 minus C presuperscript n subscript 3 plus C presuperscript n subscript 4.... C presuperscript n subscript 0 plus C presuperscript n subscript 2 plus C presuperscript n subscript 4... equals C presuperscript n subscript 1 plus C presuperscript n subscript 3 plus C presuperscript n subscript 5 plus.... rightwards arrow circle enclose 2 f r o m space circle enclose 1 space w e space h a v e 2 to the power of n equals left parenthesis C presuperscript n subscript 0 plus C presuperscript n subscript 2 plus C presuperscript n subscript 4 plus.... right parenthesis plus left parenthesis C presuperscript n subscript 1 plus C presuperscript n subscript 3 plus C presuperscript n subscript 5 plus... right parenthesis 2 to the power of n equals 2 left parenthesis C presuperscript n subscript 0 plus C presuperscript n subscript 2 plus C presuperscript n subscript 4 plus.... right parenthesis space space space left square bracket f r o m space circle enclose 2 right square bracket left parenthesis C presuperscript n subscript 0 plus C presuperscript n subscript 2 plus C presuperscript n subscript 4 plus.... right parenthesis equals 2 to the power of n minus 1 end exponent$