2.{1/9.10+1/10.11+1/11.12+.............+1/x.(x+1)=1/9
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2 . ( \(\frac{1}{9.10}\)+ \(\frac{1}{10.11}\)+\(\frac{1}{11.12}\)+..............+\(\frac{1}{x.\left(x+1\right)}\)) = \(\frac{1}{9}\)
1/7.8+1/8.9+1/9.10+1/10.11+1/11.12+1/12.13
\(\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}\)
\(=\frac{8-7}{7\cdot8}+\frac{9-8}{8\cdot9}+\frac{10-9}{9\cdot10}+\frac{11-10}{10\cdot11}+\frac{12-11}{11\cdot12}+\frac{13-12}{12\cdot13}\)
\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}\)
\(=\frac{1}{7}-\frac{1}{13}=\frac{13-7}{7\cdot13}=\frac{6}{91}\)
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\(\frac{6}{91}\)nha
2. (1/10.11+1/11.12+...+1/x.(x+1))=1/9
Tìm X thuộc N biết :
2 . ( 1/9.10 + 1/10.11 + 1/11.12 + ... + 1/x<x+1>)
Tính giúp mình với
Ai nhanh mình ticks cho , bao nhiêu tick cũng được
Giúp mình nhé
co \(\frac{1}{9\cdot10}=\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{10\cdot11}=\frac{1}{10}-\frac{1}{11}\)
............
\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}-\frac{1}{x+1}\)
nen \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\)
\(=\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}-...+\frac{1}{x}-\frac{1}{x+1}\)
=\(\frac{1}{9}-\frac{1}{x+1}\)
2 . ( \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\))
= 2 . ( \(\frac{1}{9}-\frac{1}{x+1}\)) = \(\frac{2}{9}-\frac{2}{x+1}\)
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1/9.10 + 1/10.11 + 1/11.12 + ............. + 1/9999.10000 = ?
hãy tính nhanh
nhớ giải chi tiết nhé
Tìm x biết: \(x.\left(\frac{2015}{8.9}+\frac{1925}{9.10}+\frac{1795}{10.11}+\frac{1629}{11.12}+6\right)=\frac{1}{24}\)
Bài 1.Tìm x, biết:
\(2.\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1}{9}\)
\(\left|x\right|-\frac{3}{4}=\frac{5}{3}\)
Bài 2. Lớp 6A có một số HS biết số HSG là 8 HS. Số HS trung bình = \(\frac{3}{10}\)số học sinh cả lớp. Tính số HS khá của lớp 6A
\(2\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1}{9}\)
\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{1}{9}\)
\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{x+1}\right)=\frac{1}{9}\)
\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{9}\div2\)
\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{9}-\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow x+1=18\)
\(\Leftrightarrow x=18-1\)
\(\Leftrightarrow x=17\)
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\(\left|x\right|-\frac{3}{4}=\frac{5}{3}\)
\(\Leftrightarrow\left|x\right|=\frac{5}{3}+\frac{3}{4}\)
\(\Leftrightarrow\left|x\right|=\frac{20}{12}+\frac{9}{12}\)
\(\Leftrightarrow\left|x\right|=\frac{29}{12}\)
\(\Leftrightarrow x=\pm\frac{29}{12}\)
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Bài 1 :
\(2.\left(\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{x.\left(x+1\right)}\right)\)= \(\frac{1}{9}\)
=> \(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+1}\)= \(\frac{1}{18}\)
\(\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)
\(\frac{1}{x+1}=\frac{1}{18}\)
=> x + 1 = 18
=> x = 17
vậy x = 17
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Xem thêm câu trả lời
1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11+1/11.12+1/12.13+1/13.14+1/14.15
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\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{13\cdot14}+\frac{1}{14\cdot15}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{14}-\frac{1}{15}\)
\(=\frac{1}{2}-\frac{1}{15}\)
\(=\frac{13}{30}\)
9.10+10.11+11.12+...+1000.1001
