Giả pt
(1+\(\frac{1}{1.3}\))(1+\(\frac{1}{2.4}\))(1+\(\frac{1}{3.5}\))...(\(1+\frac{1}{x\left(x+2\right)}\))=\(\frac{31}{16}\)
Những câu hỏi liên quan
GPT:
\(y=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).......\left(1+\frac{1}{x\left(x+2\right)}\right)=\frac{31}{16}\)
Tìm x, biết \(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)....\left(1+\frac{1}{x\left(x+2\right)}\right)=\frac{4016}{2007}\)
Giải phương trình:1.frac{x-5}{x-5}+frac{x-6}{x-5}+frac{x-7}{x-5}+...+frac{1}{x-5}4left(xin Nright)2.frac{1}{x^2+3x+2}+frac{1}{x^2+5x+6}+frac{1}{x^2+7x+12}+...+frac{1}{x^2+15x+56}frac{1}{14}3.left(1+frac{1}{1.3}right)left(1+frac{1}{2.4}right)left(1+frac{1}{3.5}right)...left(1+frac{1}{xleft(x+2right)}right)frac{31}{16}left(xin Nright)4.8left(x^2+frac{1}{x^2}right)-34left(x+frac{1}{x}right)+5105.6x^4-5x^3-38x^2-5x+60
Đọc tiếp
Giải phương trình:
1.\(\frac{x-5}{x-5}+\frac{x-6}{x-5}+\frac{x-7}{x-5}+...+\frac{1}{x-5}=4\left(x\in N\right)\)
2.\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+...+\frac{1}{x^2+15x+56}=\frac{1}{14}\)
3.\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{x\left(x+2\right)}\right)=\frac{31}{16}\left(x\in N\right)\)
4.\(8\left(x^2+\frac{1}{x^2}\right)-34\left(x+\frac{1}{x}\right)+51=0\)
5.\(6x^4-5x^3-38x^2-5x+6=0\)
a) Tìm x : \(\frac{x-214}{86}+\frac{x-132}{84}+\frac{x-54}{82}=6\)
b) Tính : \(\frac{1}{2}\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2015.2017}\right)\)
a: \(\Leftrightarrow\dfrac{x-214}{86}-1+\dfrac{x-132}{84}-2+\dfrac{x-54}{82}-3=0\)
=>x-300=0
hay x=300
Đúng 0
Bình luận (0)
tính : \(\frac{1}{2}.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right).....\left(1+\frac{1}{2015.2017}\right)\)
\(\frac{1}{2}.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2015.2017}\right)\)
\(=\frac{1}{2}.\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}...\frac{2015.2017+1}{2015.2017}\)
\(=\frac{1}{2}.\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{2016.2016}{2015.2017}\)
\(=\frac{1}{2}.\frac{2.3.4...2016}{1.2.3...2015}.\frac{2.3.4...2016}{3.4.5...2017}\)
\(=\frac{1}{2}.2016.\frac{2}{2017}=\frac{2016}{2017}\)
Đúng 0
Bình luận (1)
Tính \(\frac{1}{2}.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)....\left(1+\frac{1}{2015.2017}\right)\)
\(\frac{1}{2}.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2015.2017}\right)\)
\(=\frac{1}{2}.\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}...\frac{2015.2017+1}{2015.2017}\)
\(=\frac{1}{2}.\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{2016.2016}{2015.2017}\)
\(=\frac{1}{2}.\frac{2.3.4...2016}{1.2.3...2015}.\frac{2.3.4...2016}{3.4.5...2017}\)
\(=\frac{1}{2}.2016.\frac{2}{2017}=\frac{2016}{2017}\)
Đúng 0
Bình luận (0)
giúp mik với, t4 mik đi hc rùi
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).......\left(1+\frac{1}{2014.2016}\right)=\frac{x}{1008}\)
Rút gọn :\(A=\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+...+\frac{1}{\left(2n-1\right)\left(2n+1\right)}+\frac{1}{2n\left(2n+2\right)}\)
tự làm là hạnh phúc của mỗi công dân.
\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)....\left(1+\frac{1}{20.22}\right)\)
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{20.22}\right)\)
\(=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}.....\frac{20.22+1}{20.22}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{21^2}{20.22}\)
\(=\frac{\left(2.3.4.....21\right)\left(2.3.4.....21\right)}{\left(1.2.3.....20\right)\left(3.4.5.....22\right)}\)
\(=\frac{21.2}{22}=\frac{42}{22}=\frac{21}{11}\)
Đúng 0
Bình luận (0)