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NQ
4
BN
19 tháng 5 2016
\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)
\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)
\(M=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)
\(M=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)
\(M=2\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(M=2\times\frac{8}{45}\)
\(M=\frac{16}{45}\)
PA
19 tháng 5 2016
\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)
\(M=\frac{1\times2}{15\times2}+\frac{1\times2}{21\times2}+\frac{1\times2}{28\times2}+\frac{1\times2}{946\times2}+\frac{1\times2}{990\times2}\)
\(M=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{1892}+\frac{2}{1980}\)
\(M=2\times\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\right)\)
\(M=2\times\left(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{43\times44}+\frac{1}{44\times45}\right)\)
\(M=2\times\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)
\(M=2\times\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(M=2\times\left(\frac{9}{45}-\frac{1}{45}\right)\)
\(M=2\times\frac{8}{45}\)
\(M=\frac{16}{45}\)
Chúc bạn học tốt
MN
Tính tổng ;
M = \(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+.....+\frac{1}{946}+\frac{1}{990}\)
HELP ME
3
TM
15 tháng 5 2016
\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\right)\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{43.44}+\frac{1}{44.45}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{45}=\frac{9}{45}-\frac{1}{45}=\frac{8}{45}\)
\(\Rightarrow M=\frac{8}{45}:\frac{1}{2}=\frac{8}{45}.2=\frac{16}{45}\)
nhớ ấn đúng cho mình nha
TN
15 tháng 5 2016
\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)
\(=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=2\times\frac{8}{45}\)
\(=\frac{16}{45}\)
15 tháng 5 2016
Chào bạn, bạn hãy theo dõi bài giải của mình nhé!
\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)
\(=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{1892}+\frac{2}{1980}\)
\(=\frac{2}{5\cdot6}+\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+...+\frac{2}{43\cdot44}+\frac{2}{44\cdot45}\)
\(=2\left(\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{43\cdot44}+\frac{1}{44\cdot45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{45}\right)=2\left(\frac{9}{45}-\frac{1}{45}\right)=2\cdot\frac{8}{45}=\frac{16}{45}\)
Chúc bạn học tốt!
2 tháng 4 2017
21)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)
W
6 tháng 5 2015
phaỉ giải chi tiết chứ nói như nguyentuantai thì bấm áy tính cũng ra thôi!
6 tháng 5 2015
\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)
\(=2\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(=2\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
\(=2\left(\left[\frac{1}{3}-\frac{1}{4}\right]+\left[\frac{1}{4}-\frac{1}{5}\right]+\left[\frac{1}{5}-\frac{1}{6}\right]+\left[\frac{1}{6}-\frac{1}{7}\right]+\left[\frac{1}{7}-\frac{1}{8}\right]+\left[\frac{1}{8}-\frac{1}{9}\right]+\left[\frac{1}{9}-\frac{1}{10}\right]\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{10}\right)\)
\(=2\cdot\frac{7}{30}\)
\(=\frac{7}{15}\)
NH
1
21 tháng 4 2016
- 2.s= 1/30+1/42+1/56+...+ 1/380
2.S= 1/ 5.6 =1/ 6.7 +1/ 7.8 +...+1/ 19.20
2.S= 1/5-1/20
2S= 3/20
\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)
\(M=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)
\(M=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)
\(M=2\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(M=2\times\frac{8}{45}\)
\(M=\frac{16}{45}\)
\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+....+\frac{1}{946}+\frac{1}{990}\)
\(M=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+.....+\frac{2}{1892}+\frac{2}{1980}\)
\(M=2.\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\right)\)
\(M=2.\left(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+....+\frac{1}{43.44}+\frac{1}{44.45}\right)\)
\(M=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\right)\)
\(M=2.\left(\frac{1}{5}-\frac{1}{45}\right)=2.\frac{8}{45}=\frac{16}{45}\)
Vậy M=16/45