Tính tổng :
A= 1/3+1/6+1/10+1/15+...+1/45.
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DL
13 tháng 5 2019
Ta co:
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{72}+\frac{1}{90}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}+\frac{1}{9.10}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\Rightarrow A=\frac{13}{10}.\)
13 tháng 5 2019
\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)
\(A=\frac{2}{4}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{72}+\frac{2}{90}\)
\(A=\frac{2}{2.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{8.9}+\frac{2}{9.10}\)
\(A=2\left(\frac{1}{2.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(A=2.\frac{2}{5}\)
\(A=\frac{4}{5}\)
~ Học tốt ~ K cho mk nhé! Thank you.
DN
4
15 tháng 4 2018
đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45
A*2=(1/6*+1/10+1/15+1/21+1/28+1/36+1/45)*2
A*2=1/12+1/20+1/30+1/42+1/56+1/72+1/90
A*2=1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
A*2=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-/8+1/8-1/9+1/9-1/10
A*2=1/3-1/10
A*2=7/30
A=7/30 / 2
A=7/15
DN
2
15 tháng 4 2018
đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45
6A=1+3/5+2/5+2/7+3/14+1/6+2/15
6A=1+1+7/14+1/6+2/15
6A=14/5
A=14/5:6=7/15
VB
1
TM
13 tháng 4 2015
a) thấy dấu cộng ở trước số 6 thành dấu trừ
b) = 2/ 2 + 2/ 6 + 2/ 12 + 2/ 20 + 2/ 30 + 2/ 42 + 2/ 56 + 2/ 72 + 2/ 90
= 2x ( 1/ 1x2 + 1 / 2x3 + 1/ 3x4 + 1/ 4x5 + 1/ 5x6 + 1/ 6x7 + 1/ 7x8 + 1/ 8x9 + 1/ 9x10 )
= 2x ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +1/5 - 1/6 +.. + 1/8- 1/9 + 1/9 - 1/10 )
=2 x( 1 - 1/10 )
=2 x 9/10 = 18/10 = 9 / 5
TN
4
12 tháng 4 2019
bn ơi bài này ko có 1/4 đâu:
đặt A=\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{36}+\)\(\frac{1}{45}\)
\(\frac{1}{2}A\)=> \(\frac{1}{2}A\)= \(\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)
\(\frac{1}{2}A\)= \(\frac{1}{4}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(\frac{1}{2}A\)= \(\frac{1}{4}\)+ \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}A\)= \(\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{5}{20}+\frac{10}{20}-\frac{2}{20}=\frac{13}{20}\)
=> A = \(\frac{13}{20}:\frac{1}{2}=\frac{13}{10}\)
Chúc bn học tốt !
LC
3
8 tháng 8 2020
Bài làm:
Ta có: \(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{66}\)
\(=\frac{1}{1}+\frac{1}{1.3}+\frac{1}{3.2}+...+\frac{1}{11.6}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.1.3}+\frac{1}{2.3.2}+...+\frac{1}{2.11.6}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{12}\right)\)
\(=\frac{1}{2}.\frac{11}{12}\)
\(=\frac{11}{24}\)
NH
8 tháng 8 2020
\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}+\frac{1}{66}\)
\(=\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{9\times10}+\frac{1}{10\times11}+\frac{1}{11\times12}\right)\)
\(=2\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\right)\)
\(=2\times\left(1-\frac{1}{12}\right)\)
\(=2\times\frac{11}{12}\)
\(=\frac{11}{6}\)
NH
3
28 tháng 6 2016
Nhân cả tử cả mẫu của các phân số trong A với 2 ta có:
\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..........+\frac{2}{90}\)
\(=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.........+\frac{1}{90}\right)\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+........+\frac{1}{9.10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2.\frac{2}{5}\)
\(=\frac{4}{5}\)
28 tháng 6 2016
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(A=\frac{2}{5}\)
CT
1
21 tháng 3 2024
=2×(16+112+120+130+...+1
=2×(12×3+13×4+14×5+...+L2×(2×31+3×41+4×51+...+9×101)
=2×(12−13+13−14+14−15+...+19−1
=45
A = \(\frac13\) + \(\frac16\) + \(\frac{1}{10}\) + \(\frac{1}{15}\) + ... + \(\frac{1}{45}\)
A = \(\frac26\) + \(\frac{2}{12}\) + \(\frac{2}{20}\) + \(\frac{2}{30}\) + ... + \(\frac{2}{90}\)
A = 2.(\(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) + \(\frac{1}{4.5}\) + ... + \(\frac{1}{9.10}\))
A = 2.(\(\frac12-\frac13\) + \(\frac13-\frac14\) +\(\frac14-\) \(\frac15\) + ... + \(\frac19\) - \(\frac{1}{10}\))
A = 2.(\(\frac12-\frac{1}{10}\))
A = 2.\(\frac25\)
A = \(\frac45\)