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HN
1
26 tháng 7 2018
\(1)\frac{11}{12}-\frac{5}{12}\left(0,8-\frac{1}{10}\right):\left(-\frac{7}{12}\right)\)
\(=\frac{11}{12}-\frac{5}{12}\times\frac{7}{10}:\left(-\frac{7}{12}\right)\)
\(=\frac{11}{12}-\frac{7}{24}:\left(-\frac{7}{12}\right)\)
\(=\frac{11}{12}-\left(-\frac{1}{2}\right)\)
\(=\frac{17}{12}\)
12 tháng 7 2018
\(\frac{1}{7\cdot12}+\frac{1}{12\cdot17}+...+\frac{1}{2017\cdot2022}\)
\(=\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+...+\frac{5}{2017\cdot2022}\right)\)
\(=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{2}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)
\(=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{2022}\right)\)
\(=\frac{1}{4}\cdot\frac{2015}{14154}\)
\(=\frac{2015}{56616}\)
MS
1
N
30 tháng 11 2018
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{12}\left(1+2+3+...+12\right)\)
\(B=1.\left(\frac{1.2}{2}\right)+\frac{1}{2}.\left(\frac{2.3}{2}\right)+\frac{1}{3}.\left(\frac{3.4}{2}\right)+....+\frac{1}{12}.\left(\frac{12.13}{2}\right)\)
\(B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+....+\frac{13}{2}=\frac{2+3+4+....+13}{2}=\frac{90}{2}=45\)
GA
1
11 tháng 6 2022
\(=\left(\dfrac{1}{12}+\dfrac{11}{12}\right)+\left(\dfrac{1}{5}-\dfrac{6}{5}\right)+\dfrac{1}{71}=1-1+\dfrac{1}{71}=\dfrac{1}{71}\)
KS
0
DH
chứng minh rằng A= 12/1*4*7+12/4*7*10+12/7*10*13+...+12/54*57*60<1/2
giải giup minh nha minh tich cho
2
17 tháng 2 2017
////????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????không biết
21 tháng 11 2017
\(\dfrac{12}{1.4.7}+\dfrac{12}{4.7.10}+\dfrac{12}{7.10.13}+...+\dfrac{12}{54.57.60}\)
\(=2\left(\dfrac{1}{1.4}-\dfrac{1}{4.7}+\dfrac{1}{4.7}-\dfrac{1}{7.10}+\dfrac{1}{7.10}-\dfrac{1}{10.13}+...+\dfrac{1}{54.57}-\dfrac{1}{57.60}\right)\)\(=2\left(\dfrac{1}{1.4}-\dfrac{1}{57.60}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{57.60}\right)=\dfrac{1}{2}-\dfrac{1}{2.57.60}< \dfrac{1}{2}\left(đpcm\right)\)
CN
1
NH
20 tháng 6 2019
a,\(\frac{11}{12}-\left(\frac{5}{42}-x\right)=\frac{15}{28}-\frac{11}{12}\)
\(\Leftrightarrow\frac{11}{12}-\frac{5}{42}+x=\frac{15}{28}-\frac{11}{12}\)
\(\Leftrightarrow x=\frac{15}{28}-\frac{11}{12}-\frac{11}{12}+\frac{5}{42}\)
\(\Leftrightarrow x=\left(\frac{15}{28}+\frac{5}{42}\right)-\left(\frac{11}{12}+\frac{11}{12}\right)\)
\(\Leftrightarrow x=\frac{55}{84}-\frac{11}{6}\)
\(\Leftrightarrow x=\frac{-33}{28}\)
b, \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
NT
3
N
4 tháng 12 2018
\(M=54-\frac{1}{2}.\left(1+2\right)-\frac{1}{3}.\left(1+2+3\right)-....-\frac{1}{12}.\left(1+2+...12\right)\)
\(M=54-\left[\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+....+\frac{1}{12}.\left(1+2+...+12\right)\right]\)
\(M=54-\left(\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+....+\frac{1}{12}\cdot\frac{12.13}{2}\right)\)
\(M=54-\left(\frac{3}{2}+\frac{4}{2}+...+\frac{13}{2}\right)=54-44=10\)
Vậy M=10
TL
13
HT
@NGHĨA
TL:
1+12=13
-HT-