Tính:\(\frac{1}{x}+\frac{1}{x+1}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}+\frac{32}{1+x^{32}}\)
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Thực hiện phép tính :
\(\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}+\frac{32}{1+x^{32}}\)
khó quá làm sao mà trả lời đc
tự đầu mình vắt óc mà suy nghĩ
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Given that
\(\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}-\frac{16}{x^{16}+1}=\frac{a}{x^{32}-1}\)
for all \(x\ne-1;1\).What is the value of a ?
tính:
\(\frac{1}{1-x}+\frac{1}{x+1}+\frac{2}{x^2+1}+\frac{4}{x^4+1}+\frac{8}{x^8+1}+\frac{16}{x^{16}+1}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=\frac{1}{x}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(=1-\frac{1}{32}\)
\(=\frac{31}{32}\)
có tử = 1 thì k bt à nha
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Đặt: \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(\Rightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(\Rightarrow\)\(A=1-\frac{1}{32}=\frac{31}{32}\)
mà \(A=\frac{1}{x}\)
nên \(\frac{1}{x}=\frac{31}{32}\)
\(\Rightarrow\)\(x=\frac{32}{31}\)
Vậy...
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\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}.\)
\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)+\left(\frac{1}{16}+\frac{1}{32}\right)\)
\(=\frac{7}{8}+\frac{3}{32}\)
\(=\frac{31}{32}\)
\(\Leftrightarrow x\)không tồn tại
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Xem thêm câu trả lời
thực hiên phép tính:
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{1}{1+x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
Bài 1: Thưch hiện phép tính:
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
= 1+x+1--x/1-x^2 +2/1+x^2+....+16/1+x^26
= 2/1-x^2+2/1+x^2+....+16/1+x^16
= ........
= 16/1-x^16 + 16/1+x^16
= 16+16x^16+16-16x^16/1-x^32
= 32/1-x^32
k mk nha
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ĐKXĐ: \(x\ne\pm1\)
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4}{1-x^4}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{8}{1-x^8}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{16}{1-x^{16}}+\frac{16}{1+x^{16}}\)
\(=\frac{32}{1-x^{32}}\)
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tính :
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
2y-\(\frac{6xy+2y}{3x+2y}+\frac{2y-9x^2}{3x+2y}\)
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
thực hiện phép tính \(A=\frac{1}{x-1}-\frac{1}{x-1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}-\frac{16}{x^{16}+1}\)