s= \(\dfrac{1}{5x9}\)+\(\dfrac{1}{9x13}\)+....+\(\dfrac{1}{41x45}\)
Những câu hỏi liên quan
Tìm x:
\(\dfrac{7}{x}\)+\(\dfrac{4}{5x9}\)+\(\dfrac{4}{9x13}\)+.....+\(\dfrac{4}{41x45}\)=\(\dfrac{29}{45}\)
\(\Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{29}{45}\left(x\ne0\right)\\ \Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}+\dfrac{8}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}=\dfrac{21}{45}\Rightarrow\dfrac{21}{3x}=\dfrac{21}{45}\Rightarrow3x=45\\ \Rightarrow x=15\)
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\(\dfrac{1}{1x5}\)+\(\dfrac{1}{5x9}\)+\(\dfrac{1}{9x13}\)+....+\(\dfrac{1}{45x49}\)
Tính nha
\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)
\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)
\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)
\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)
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Tính :
S=1/5x9 + 1/9x13 + 1/13x17 + ... + 1/41x45
\(S=\frac{1}{4}\times\left(\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+...+\frac{4}{41\times45}\right)\)
\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)\)
\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(S=\frac{1}{4}\times\frac{8}{45}\)
\(S=\frac{1\times2}{1\times45}\)
\(S=\frac{2}{45}\)
Vậy \(S=\frac{2}{45}\)
Tk nha bn !!
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mình nhầm , kết quả là \(\frac{2}{45}\)
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Xem thêm câu trả lời
Tính:
(2007 - 2005) + (2003 - 2001) +...+ (7 - 5) + (3 - 1)
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Viết tiếp 3 số hạng thứ 8;9 và 10 của dãy số sau: \(\dfrac{1}{1x5};\dfrac{1}{5x9};\dfrac{1}{9x13};...\)
\(\dfrac{4}{1x5}\) \(+\) \(\dfrac{4}{5x9}\) \(+\) \(\dfrac{4}{9x13}\) \(+\) ... \(+\) \(\dfrac{4}{53x57}\)
I=\(\dfrac{2}{1x5}\)+\(\dfrac{2}{5x9}\)+\(\dfrac{2}{9x13}\)+.....+\(\dfrac{2}{181x185}\)
\(I=\dfrac{2}{1\times5}+\dfrac{2}{5\times9}+\dfrac{2}{9\times13}+...+\dfrac{2}{181\times185}\)
\(=\dfrac{1}{2}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{181\times185}\right)\)
\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{181}-\dfrac{1}{185}\right)\)
\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{185}\right)=\dfrac{1}{2}\times\dfrac{184}{185}=\dfrac{92}{185}\)
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Adfrac{8}{1x5}+dfrac{8}{5x9}+dfrac{8}{9x13}+.....+dfrac{8}{25x29}
Bdfrac{3}{5x8}xdfrac{11}{8x9}+dfrac{12}{19x31}+dfrac{70}{31x101}+dfrac{99}{101x200}
Cdfrac{1}{8}+dfrac{1}{104}+dfrac{1}{234}+dfrac{1}{414}+dfrac{1}{644}+dfrac{1}{924}+dfrac{1}{1254}
Giúp mik với!! trước sáng mai nha, mik cần gấp lắm!! Cái này toán nâng cao nha, mik cảm ơn
Đọc tiếp
A=\(\dfrac{8}{1x5}+\dfrac{8}{5x9}+\dfrac{8}{9x13}+.....+\dfrac{8}{25x29}\)
B=\(\dfrac{3}{5x8}x\dfrac{11}{8x9}+\dfrac{12}{19x31}+\dfrac{70}{31x101}+\dfrac{99}{101x200}\)
C=\(\dfrac{1}{8}+\dfrac{1}{104}+\dfrac{1}{234}+\dfrac{1}{414}+\dfrac{1}{644}+\dfrac{1}{924}+\dfrac{1}{1254}\)
Giúp mik với!! trước sáng mai nha, mik cần gấp lắm!! Cái này toán nâng cao nha, mik cảm ơn
Tính nhanh 1x5+5x9+9x13+...+41x45
làm bừa thui,ai tích mình mình tích lại
Số số hạng là :
Có số cặp là :
50 : 2 = 25 ( cặp )
Mỗi cặp có giá trị là :
99 - 97 = 2
Tổng dãy trên là :
25 x 2 = 50
Đáp số : 50
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A = 1.5 + 5.9 + 9.13 + ...+ 41.45
A = \(\dfrac{12}{12}\).(1.5 + 5.9 + 9.13 +...+ 41.45)
A = \(\dfrac{1}{12}\).(1.5.12 + 5.9.12 + 9.13.12 + ... + 41.45.12)
A = \(\dfrac{1}{12}\).[1.5.(9 + 3) + 5.9.(13 - 1) + 9.13.(17 - 5) + ... + 41.45.(49 - 37)]
A = \(\dfrac{1}{12}\)[1.5.9 + 1.5.3 + 5.9.13 - 1.5.9 + 9.13.17 - 5.9.13 +...+41.45.49 - 41.45.37]
A =\(\dfrac{1}{12}\).[1.5.3 + 41.45.49]
A = \(\dfrac{1}{12}\).[15 + 90405]
A = \(\dfrac{1}{12}\).90420
A = 7535
.
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Tìm x,biết:
a) 7/x + 4/5x9 + 4/9x13 + .....+ 4/41x45 = 29/45
b) x/2008 - (1/10 + 1/15 + 1/21 +..............+1/120) = 5/8
a) \(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}=\frac{29}{45}-\frac{8}{45}\)
\(\Rightarrow\frac{7}{x}=\frac{7}{15}\)
\(\Rightarrow x=15\)
Vậy x = 15
b) \(\frac{x}{2008}-\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-\left(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\right)=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-\left(\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\right)=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-2.\frac{3}{16}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}=\frac{5}{8}+\frac{3}{8}\)
\(\Rightarrow\frac{x}{2008}=1\)
\(\Rightarrow x=2008\)
Vậy x = 2008
_Chúc bạn học tốt_
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