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ali122004
@ali122004
July 2022
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запишите произведение многочленов (1+x)(1+x^2)(1+x^4)...(1+x^2048) в стандартном виде
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sedinalana
Verified answer
Домножим на 1-х и разделим на 1-х
[(1-x)(1+x)(1+x^2)(1+x^4)....(1+x^2048)}/(1-x)=
=[(1-x^2)(1+x^2)(1+x^4)....(1+x^2048)]/(1-x)=
=[(1-x^4)*(1+x^4).....(1^2048)]/(1-x)=[(1-x^8).....(1+x^2048)/(1-x)=
=(1-x^4096)/(1-x)
4 votes
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Answers & Comments
Verified answer
Домножим на 1-х и разделим на 1-х[(1-x)(1+x)(1+x^2)(1+x^4)....(1+x^2048)}/(1-x)=
=[(1-x^2)(1+x^2)(1+x^4)....(1+x^2048)]/(1-x)=
=[(1-x^4)*(1+x^4).....(1^2048)]/(1-x)=[(1-x^8).....(1+x^2048)/(1-x)=
=(1-x^4096)/(1-x)