TÍNH A : \(\left[1+\frac{1}{3x5}\right]x\left[1+\frac{1}{5x7}\right]x.......x\left[1+\frac{1}{37x39}\right]\)
tính A=[ 1+\(\frac{1}{3x5}\)] + [1+ \(\frac{1}{5x7}\)] +\(\left[1+\frac{1}{7x9}\right]\)+........+ \(\left[1+\frac{1}{37x39}\right]\)
Giải
Ta có A= [1+1/3.5] + [1+1/5.7] + [1+1/7.9] + ... + [1+1/37.39]
=>A= (1+1+1+...+1) +(1/3.5 + 1/5.7 + 1/7.9 + ... + 1/37.39)
=> A = 18 + 1/2.(2/3.5+2/5.7+2/7.9+...+2/37.39)
=>A = 18 + 1/2.(1/3-1/5+1/5-1/7+1/7-1/9+...+1/37-1/39)
=> A= 18 + 1/2.(1/3-1/39)
=> A= 18 + 1/2 . 4/13
=>A= 18 + 2/13 = 236/13
tính A=\(\frac{1}{2}\left(\frac{1}{1x3}\right)\left(\frac{1}{2x4}\right)\left(\frac{1}{3x5}\right)x....x\left(\frac{1}{2015x2017}\right)\)
Tính:
a) \(A=\left(1-\frac{1}{15}\right)x\left(1-\frac{1}{21}\right)x\left(1-\frac{1}{28}\right)x.........x\left(1-\frac{1}{1275}\right)\)
b) \(B=\left(1+\frac{1}{1x3}\right)x\left(1+\frac{1}{2x4}\right)x\left(1+\frac{1}{3x5}\right)x............x\left(1+\frac{1}{99x101}\right)\)
\(A=\left(1-\frac{1}{15}\right).\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right)......\left(1-\frac{1}{1275}\right)\)
Tìm x:
\(\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+.....+\frac{1}{19x21}\right).x=\frac{9}{7}\)
\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)x=\frac{9}{7}\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\right]x=\frac{9}{7}\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{21}\right)\right]x=\frac{9}{7}\)
\(\left(\frac{1}{2}.\frac{2}{7}\right)x=\frac{9}{7}\)
\(\frac{1}{7}.x=\frac{9}{7}\)
\(x=\frac{9}{7}\div\frac{1}{7}\)
\(x=9\)
Vậy ...
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=\(\frac{9^{1006}-1}{4}\)
Tìm x:
\(\left(x+\frac{1}{1x3}\right)+\left(x+\frac{1}{3x5}\right)+......+\left(x+\frac{1}{23x25}\right)=11.x+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{81}+\frac{1}{243}\right)\)
Help me please! Thanks a lot!
Nhân 2 cả 2 vế lên:
\(\left(2x+\frac{2}{1x3}\right)+...+\left(2x+\frac{2}{23x25}\right)=22x+\frac{2}{3}+\frac{2}{9}+\frac{2}{81}+\frac{2}{243}\)2/243
\(24x+\left(1-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{23}-\frac{1}{25}\right)=22x+\frac{162+54+6+2}{243}\)
\(24x+\frac{24}{25}=22x+\frac{224}{243}\)
\(2x=\frac{224}{243}-\frac{24}{25}\)
\(2x=-\frac{232}{6025}\)
\(x=\frac{-116}{6075}\)
\(\left(x+\frac{1}{1.3}\right)+\left(x+\frac{1}{3.5}\right)+...+\left(x+\frac{1}{23.25}\right)=11.x+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{81}+\frac{1}{243}\right)\)
\(12x+\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{23}-\frac{1}{25}\right)\right]=11.x+\left(\frac{81}{243}+\frac{27}{243}+\frac{3}{243}+\frac{1}{243}\right)\)
\(12x+\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{25}\right)\right]=11.x+\frac{112}{243}\)
\(12x+\left(\frac{1}{2}.\frac{24}{25}\right)=11.x+\frac{112}{243}\)
\(12x+\frac{12}{25}=11x+\frac{112}{243}\)
\(11x-12x=\frac{112}{243}-\frac{12}{25}\)
\(-1x=-\frac{116}{6075}\)
\(x=-\frac{116}{6075}\div\left(-1\right)\)
\(x=\frac{116}{6075}\)
\(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+......+\frac{1}{Xx\left(X+2\right)}=\frac{8}{17}\)
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
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{8}{17}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\Leftrightarrow1-\frac{1}{x+1}=\frac{16}{17}\)
\(\Leftrightarrow\frac{1}{x+2}=\frac{1}{17}\)
\(\Rightarrow x+2=17\Rightarrow x=15\)
tinh nhanh
\(\left(1-\frac{1}{1x3}\right)x\left(1-\frac{1}{2x4}\right)x\left(1-\frac{1}{3x5}\right)x....x\left(1-\frac{1}{20x22}\right)\)
ai làm được giúp mình nhé
A= (1-1/1x3)x(1-1/2x4)-(1-1/3x5)......x(1-1/20x22)
tinh nhanh
\(\left(1-\frac{1}{1x3}\right)x\left(1-\frac{1}{2x4}\right)x\left(1-\frac{1}{3x5}\right)x....x\left(1-\frac{1}{20x22}\right)\)