\(\dfrac{4}{1x5}\) \(+\) \(\dfrac{4}{5x9}\) \(+\) \(\dfrac{4}{9x13}\) \(+\) ... \(+\) \(\dfrac{4}{53x57}\)
Những câu hỏi liên quan
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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\(\dfrac{1}{1x5}\)+\(\dfrac{1}{5x9}\)+\(\dfrac{1}{9x13}\)+....+\(\dfrac{1}{45x49}\)
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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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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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: \(\dfrac{1}{1x5};\dfrac{1}{5x9};\dfrac{1}{9x13};...\)
s= \(\dfrac{1}{5x9}\)+\(\dfrac{1}{9x13}\)+....+\(\dfrac{1}{41x45}\)
\(S=\dfrac{1}{5\times9}+\dfrac{1}{9\times13}+...+\dfrac{1}{41\times45}\)
\(\Rightarrow4S=\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+...+\dfrac{4}{41\times45}\)
\(\Rightarrow4S=\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}\)
\(\Rightarrow4S=\dfrac{1}{5}-\dfrac{1}{45}\)
\(\Rightarrow4S=\dfrac{8}{45}\)
\(\Rightarrow S=\dfrac{2}{45}\)
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\(=\dfrac{1}{4}\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{41\cdot45}\right)\)
\(=\dfrac{1}{4}\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{8}{45}=\dfrac{2}{45}\)
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4/1x5 cộng 4/5x9 cộng 4/9x13 cộng 4/13x17 .
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
4/1x5 + 4/5x9 + 4/9x13 +.......+ 4/(X-4)x(X) = 15/17
a) rút gọn: \(\dfrac{4^5x9^4-2x6^9}{2^{10}x3^8+6^8x20}\)
b) Cho A=\(\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}\).So sánh A với 2
a: \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot2^2\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{-2}{6}=-\dfrac{1}{3}\)
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