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NT
0
NN
3
NH
0
14 tháng 8 2016
\(B=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{10}\)
\(B=\frac{1}{3}-\frac{1}{10}\)
\(B=\frac{7}{30}\)
15 tháng 7 2018
\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-\frac{1}{5.6}-\frac{1}{4.5}-\frac{1}{3.4}-\frac{1}{2.3}-\frac{1}{1.2}\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)+\frac{1}{9.10}\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)+\frac{1}{90}\)
\(=-\left(1-\frac{1}{10}\right)+\frac{1}{90}\)
\(=-\frac{9}{10}+\frac{1}{90}\)
= ...
bn tự tính nha!
TN
2
21 tháng 1 2017
7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8 - 17/8.9 + 19/9.10
= 3+4/3.4 - 4+5/4.5 + 5+6/5.6 - 6+7/6.7 + 7+8/7.8 - 8+9/8.9 + 9+10/9.10
=1/3 + 1/4 - 1/4 - 1/5 + 1/5 + 1/6 -1/6 - 1/7 +1/7 +1/8 - 1/8 - 1/9 + 1/9 + 1/10
=1/3 + 1/10=13/30
NH
25 tháng 7 2018
\(=\frac{6+1}{12}-\frac{10-1}{20}+\frac{10+1}{30}-\frac{14-1}{42}+\frac{14+1}{56}-\frac{18-1}{72}+\frac{18+1}{90}\)
=\(\frac{6}{12}+\frac{1}{12}-\frac{10}{20}+\frac{1}{20}+\frac{10}{30}+\frac{1}{30}-\frac{14}{42}+\frac{1}{42}+\frac{14}{56}+\frac{1}{56}-\frac{18}{72}+\frac{1}{72}+\frac{18}{90}+\frac{1}{90}\)
=\(\frac{1}{2}+\frac{1}{12}-\frac{1}{2}+\frac{1}{20}+\frac{1}{3}+\frac{1}{30}-\frac{1}{3}+\frac{1}{42}+\frac{1}{4}+\frac{1}{56}-\frac{1}{4}+\frac{1}{72}+\frac{1}{5}+\frac{1}{90}\)
\(=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{5}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{6}\)
\(=\frac{1}{3}-\frac{1}{10}+\frac{1}{5}\)
\(=\frac{10}{30}-\frac{3}{30}+\frac{6}{30}=\frac{13}{30}\)
22 tháng 10 2017
\(B=\frac{1}{3.4}-\frac{1}{4.5}-\frac{1}{5.6}-\frac{1}{6.7}-\frac{1}{7.8}-\frac{1}{8.9}-\frac{1}{9.10}\)
\(\Rightarrow B=\frac{1}{3.4}-\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(\Rightarrow B=\frac{1}{12}-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(\Rightarrow B=\frac{1}{3}-\frac{1}{4}-\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(\Rightarrow B=\frac{1}{12}-\frac{6}{40}\)
\(\Rightarrow B=\frac{-1}{15}\)
AH
25 tháng 7 2018
bạn tìm 1 số để nhân cả tử cả mẫu ra để tử ra 1 so chung nha rồi tách thôi
T
5 tháng 3 2017
đặt \(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
ta có:
\(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
\(\Leftrightarrow M=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}\) \(\Leftrightarrow M=\dfrac{3}{3.4}+\dfrac{4}{3.4}-\dfrac{4}{4.5}-\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{6}{5.6}-\dfrac{6}{6.7}-\dfrac{7}{6.7}+\dfrac{7}{7.8}+\dfrac{8}{7.8}-\dfrac{8}{8.9}-\dfrac{9}{8.9}+\dfrac{9}{9.10}+\dfrac{10}{9.10}\) \(\Rightarrow M=\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{8}+\dfrac{1}{10}+\dfrac{1}{9}\) \(\Rightarrow M=\dfrac{1}{3}+\dfrac{1}{10}\)
\(\Rightarrow M=\dfrac{10}{30}+\dfrac{3}{30}\)
\(\Rightarrow M=\dfrac{13}{30}\)
vậy M = \(\dfrac{13}{30}\)
vậy \(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{13}{30}\)
5 tháng 3 2017
\(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)
Ta có \(A=\frac{1}{3}.\frac{4}{6}.\frac{7}{9}.....\frac{208}{210}=\frac{1.4.7.....208}{3.6.9.....210}\)
Mà \(1< 3,4< 6,7< 9,...,208< 210\)
\(\Rightarrow1.4.7.....208< 3.6.9.....210\)
\(\Rightarrow\frac{1.4.7.....208}{3.6.9.....210}< 1\)\(\Leftrightarrow A< 1\)
Lại có \(1< 25\)\(\Rightarrow A< 25\)