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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... ?

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Asked by Topperlearning User 8th October 2016, 1:56 PM
Answered by 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

Answered by Expert 8th October 2016, 3:56 PM
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