Tìm X :
a) \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{11x13}+x=\frac{24}{13}\)
b)\(1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=1\frac{2009}{2011}\)
\(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+......+\frac{1}{Xx\left(X+2\right)}=\frac{8}{17}\)
Tìm x, biết x là số lẻ
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{x\left(x+2\right)}=\frac{8}{17}\)
\(\Leftrightarrow2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{x\left(x+2\right)}\right)=2.\frac{8}{17}\)
\(\Leftrightarrow\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{x\left(x+2\right)}=\frac{16}{17}\)
\(\Leftrightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+2}=\frac{16}{17}\)
\(\Leftrightarrow1-\frac{1}{x+2}=\frac{16}{17}\)
\(\Leftrightarrow\frac{1}{x+2}=1-\frac{16}{17}=\frac{1}{17}\)
\(\Rightarrow x+2=17\Rightarrow x=15\)
x là số lẻ vậy x có thể là: 1 ; 3 ; 5 ; 7 ; 9
Còn lại bạn tự giải nha! Cứ dùng phương pháp loại suy thử với từng số là ra! dễ mà
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{8}{17}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\Leftrightarrow1-\frac{1}{x+1}=\frac{16}{17}\)
\(\Leftrightarrow\frac{1}{x+2}=\frac{1}{17}\)
\(\Rightarrow x+2=17\Rightarrow x=15\)
Tìm X : \(1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=1\frac{2009}{2011}\)
=> \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2010}{2011}\)
=> \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2010}{2011}\)
=>\(1-\frac{1}{x+1}=\frac{2010}{2011}\)
=> \(\frac{1}{x+1}=\frac{2011}{2011}-\frac{2010}{2011}=\frac{1}{2011}\)
=> x + 1 = 2011
=> x = 2010
\(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+........+\frac{1}{11x13}+\frac{1}{13x15}\)
ai đúng sẽ k cho người đó
\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{13.15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
mik đã trả lời rồi mà , sao chưa hiện ra ????
\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{11\times13}+\frac{2}{13\times15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}=\frac{14}{15}\)
tìm so nguyen x biet: a) \(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+..........+\frac{1}{\left(2x-1\right)x\left(2x+1\right)}=\frac{49}{99}\)
b) 1-3+32-33+.........+(-3)x=\(\frac{9^{1006}-1}{4}\)
1)\(\frac{4}{7}:\frac{-15}{28}x\left(-3\right)^2\) 2)\(\frac{15}{49}x1,4-\left(\frac{2}{3}+\frac{4}{5}\right);\frac{22}{10}\) 3)\(\frac{1}{4}-\frac{7}{4}:\left(-7\right)-3:\frac{3}{4}x\left(-2\right)^{^2}\)
4)\(\frac{5}{1x3}+\frac{5}{3x5}+\frac{5}{5x7}+....\frac{5}{197x199}\)
ok ai giải được giúp mik nha chiều mai mik phải nộp rồi
Giải phương trình
\(\frac{1}{2}\left(\frac{2x-2}{2009}+\frac{2x}{2010}+\frac{2x+2}{2011}\right)=\frac{33}{10}-\left(\frac{x+1}{2011}+\frac{x-1}{2009}+\frac{x}{2010}\right)\)
tính A=\(\frac{1}{2}\left(\frac{1}{1x3}\right)\left(\frac{1}{2x4}\right)\left(\frac{1}{3x5}\right)x....x\left(\frac{1}{2015x2017}\right)\)
tìm x, y thỏa mãn
a, \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x.\left(x+2\right):2}=1\frac{2009}{2011}\)
Tìm x biết
a)\(\frac{x+4}{2009}+\frac{x+3}{2010}=\frac{x+2}{2011}+\frac{x+1}{2012}\)
b)\(\left(\frac{1}{4}x-1\right)\)+\(\left(\frac{5}{6}x-2\right)-\left(\frac{3}{8}x+5\right)=3,5\)
Anh chỉ giải câu a thôi, câu b anh thấy nó bình thường mà.
Cộng vào mỗi phân số thêm 1 đơn vị được:
\(\frac{x+2013}{2009}+\frac{x+2013}{2010}=\frac{x+2013}{2011}+\frac{x+2013}{2012}\).
Tới đây tự làm tiếp nhá.