Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(=1+\frac{1}{1.3}+\frac{1}{3.2}+\frac{1}{2.5}+\frac{1}{5.3}+\frac{1}{3.7}+\frac{1}{7.4}+\frac{1}{4.9}+\frac{1}{9.5}\)
\(=1+1-\frac{1}{5}\)
\(=\frac{10}{5}-\frac{1}{5}\)
\(=\frac{9}{5}\)
Ai thấy đúng thì
1/2D=1/2(1/6+1/10+......+1/45)
1/2D=1/12+1/20+1/30+.....+1/90
1/2D=1/3.4+1/4.5+1/5.6+......+1/9.10
1/2D=1/3-1/4+1/4-1/5+1/5-1/6+....+1/9-1/10
1/2D=1/3-1/10
1/2D=7/30
D=7/30:1/2
D=7/15
Ta có:\(D=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)
\(=\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}\)
\(=2.\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(=2.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=2.\left(\frac{1}{3}-\frac{1}{10}\right)=2.\frac{7}{30}=\frac{7}{15}\)
Vậy \(D=\frac{7}{15}\)
a) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{14}{30}=\frac{7}{15}\)
a)
\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=2\left(1-\frac{1}{15}\right)\)
\(=2.\frac{14}{15}\)
\(=\frac{28}{15}\)
b)
\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)
\(...\)
A=1+(1/6+1/12+1/20+...+1/90):2
A=1+(1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10):2
A=1+(1/2-1/10):2
A=1+2/5:2
A=1+1/5
A=6/5
Vậy A=6/5 nha bạn
Đúng 100%
k mk nha
Mk nhanh nhất
phaỉ giải chi tiết chứ nói như nguyentuantai thì bấm áy tính cũng ra thôi!
\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)
\(=2\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(=2\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
\(=2\left(\left[\frac{1}{3}-\frac{1}{4}\right]+\left[\frac{1}{4}-\frac{1}{5}\right]+\left[\frac{1}{5}-\frac{1}{6}\right]+\left[\frac{1}{6}-\frac{1}{7}\right]+\left[\frac{1}{7}-\frac{1}{8}\right]+\left[\frac{1}{8}-\frac{1}{9}\right]+\left[\frac{1}{9}-\frac{1}{10}\right]\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{10}\right)\)
\(=2\cdot\frac{7}{30}\)
\(=\frac{7}{15}\)
A = ( 1/3 - 1).( 1/6 - 1).( 1/10 - 1).( 1/15 - 1).( 1/21 - 1).( 1/28 - 1).( 1/36 - 1)
A = -2/3 . ( -5/6) . ( -9/10) . ( -14/15) . ( -20/21) . ( -27/28) . ( -35/36)
Do tích A có lẻ thừa số, mỗi thừa số đều mang dấu âm nên A mang dấu âm
A = -[ 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36]
Đặt B = 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36
B = 4/6 . 10/12 . 18/20 . 28/30 . 40/42 . 54/56 . 70/72
B = 1.4/2.3 . 2.5/3.4 . 3.6/4.5 . 4.7/5.6 . 5.8/6.7 . 6.9/7.8 . 7.10/8.9
B = 1.2.3.4.5.6.7/3.4.5.6.7.8.9 . 4.5.6.7.8.9.10/2.3.4.5.6.7.8
B = 2/8.9 . 9.10/2.3
B = 5/12
A = -5/12
\(=\frac{-2}{3}\cdot\frac{-5}{6}\cdot\frac{-9}{10}\cdot\cdot\cdot\cdot\frac{-35}{36}\)
\(=\frac{-4}{6}\cdot\frac{-10}{12}\cdot\frac{-18}{20}\cdot\cdot\cdot\cdot\frac{-70}{72}\)
\(=\frac{-1.4}{2.3}\cdot\frac{-2.5}{3.4}\cdot\frac{-3.6}{4.5}\cdot\cdot\cdot\cdot\frac{-7.10}{8.9}\)
\(=\frac{\left(-1\right).\left(-2\right).\left(-3\right)...\left(-7\right)}{2.3.4....8}\cdot\frac{4.5.6....10}{3.4.5....9}\)
\(=\frac{\left(-1\right).2.3...7}{2.3.4....8}\cdot\frac{10}{3}\)
\(=\frac{-1}{8}\cdot\frac{10}{3}=\frac{-5}{12}\)
=1+2/6+2/12+2/20+2/30+2/42+2/56
=1+(2.(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8))
=1+(2(1/2+1/3-1/4+....+1/7-1/8))
=1+(2.(1/2-1/8))
=1+(2.3/8)
=1+3/4
=7/4
15/16=
= 7/4 nha