\(\frac{2}{4\cdot11};\frac{2}{11\cdot18};\frac{2}{18\cdot25},...\)
a, tìm số tổng quát
b, Tính tổng 100 số hạng đầu của dãy
K
Khách
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Những câu hỏi liên quan
24 tháng 8 2020
\(\frac{1}{2.15}+\frac{3}{2.11}+\frac{4}{1.11}+\frac{5}{1.2}\)
\(=\frac{1}{30}+\left(\frac{3}{22}+\frac{4}{11}\right)+\frac{5}{2}\)
\(=\frac{1}{30}+\frac{1}{2}+\frac{5}{2}\)
\(=\frac{1}{30}+3\)
\(=\frac{91}{30}\)
24 tháng 8 2020
Đặt \(A=\frac{1}{2\cdot15}+\frac{3}{2\cdot11}+\frac{4}{1\cdot11}+\frac{5}{1\cdot2}\)
\(\Leftrightarrow\frac{A}{7}=\frac{1}{14\cdot15}+\frac{3}{11\cdot14}+\frac{4}{7\cdot11}+\frac{5}{7\cdot2}\)
\(\Leftrightarrow\frac{A}{7}=\frac{1}{14}-\frac{1}{15}+\frac{1}{11}-\frac{1}{14}+\frac{1}{7}-\frac{1}{11}+\frac{1}{2}-\frac{1}{7}\)
\(\Leftrightarrow\frac{A}{7}=-\frac{1}{15}+\frac{1}{2}=\frac{1}{2}-\frac{1}{15}=\frac{15-2}{30}=\frac{13}{70}\)
hay \(A=\frac{13\cdot7}{70}=\frac{91}{70}=\frac{13}{10}\)
6 tháng 8 2016
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}\)
\(=\frac{1}{3}-\frac{1}{143}\)
\(=\frac{140}{429}\)
TT
\(B=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}+\frac{13}{15\cdot4}\)
1
15 tháng 6 2018
\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(\frac{B}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
\(\frac{B}{7}=\frac{1}{2}-\frac{1}{28}\)
\(\frac{B}{7}=\frac{13}{28}\)
\(B=\frac{13}{28}.7=\frac{13}{4}\)
S
26 tháng 4 2017
E=\(\frac{5}{1.2}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
E.\(\frac{1}{7}\)=\(\frac{5}{1.2.7}+\frac{4}{1.11.7}+\frac{3}{11.2.7}+\frac{1}{2.15.7}+\frac{13}{15.4.7}\)
E.\(\frac{1}{7}\)=\(\frac{5}{7.2}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
E.\(\frac{1}{7}\)=\(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
E.\(\frac{1}{7}\)=\(\frac{1}{2}-\frac{1}{28}\)
E.\(\frac{1}{7}=\frac{13}{28}\)
E=\(\frac{13}{28}:\frac{1}{7}=\frac{13}{4}\)
26 tháng 4 2017
\(E=\frac{5}{1.2}+\frac{1}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(E=\frac{5}{2}+\frac{1}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}\)
\(E=\frac{5}{2}+\left(\frac{1}{11}+\frac{3}{22}\right)+\left(\frac{1}{30}+\frac{13}{60}\right)\)
\(E=\frac{5}{2}+\left(\frac{2}{22}+\frac{3}{22}\right)+\left(\frac{2}{60}+\frac{13}{60}\right)\)
\(E=\frac{5}{2}+\frac{5}{22}+\frac{15}{60}\)
\(E=\frac{55}{22}+\frac{5}{22}+\frac{1}{4}\)
\(E=\frac{60}{22}+\frac{1}{4}\)
\(E=\frac{30}{11}+\frac{1}{4}\)
\(E=\frac{120}{44}+\frac{11}{44}\)\(=\frac{131}{44}\)
k mình nha chúc bạn học giỏi
D
2
HT
9 tháng 10 2020
\(A=\frac{4}{3\cdot5}+\frac{4}{5\cdot7}+\frac{4}{7\cdot9}+\frac{4}{9\cdot11}\)
\(A=\frac{2\cdot2}{3\cdot5}+\frac{2\cdot2}{5\cdot7}+\frac{2\cdot2}{7\cdot9}+\frac{2\cdot2}{9\cdot11}\)
\(A=2\cdot\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\right)\)
\(A=2\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(A=2\cdot\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(A=2\cdot\frac{8}{33}\)
\(A=\frac{16}{33}\)
9 tháng 10 2020
Ta có:
\(A=\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}\)
\(A=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(A=2\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(A=2\cdot\frac{8}{33}\)
\(A=\frac{16}{33}\)
BT
28 tháng 3 2018
\(B=\frac{5}{2}+\left(\frac{4}{1.11}+\frac{3}{11.2}\right)+\left(\frac{1}{2.15}+\frac{13}{15.4}\right)\)
\(B=\frac{5}{2}+\frac{1}{11}.\left(4+\frac{3}{2}\right)+\frac{1}{15}\left(\frac{1}{2}+\frac{13}{4}\right)=\frac{5}{2}+\frac{1}{11}.\frac{11}{2}+\frac{1}{15}.\frac{15}{4}\)
=> \(B=\frac{5}{2}+\frac{1}{2}+\frac{1}{4}=\frac{10}{4}+\frac{2}{4}+\frac{1}{4}=\frac{13}{4}\)
28 tháng 3 2018
Ta có
1/7.B = 5/2.7 + 4/7.11 + 3/11.14 + 1/14.15 + 13/15.28
1/7.B = 1/2 - 1/7 + 1/7 - 1/11 + 1/11 - 1/14 + 1/14 - 1/15 + 1/15 - 1/28
1/7.B = 1/2 - 1/28
1/7.B = 14/28 - 1/28
1/7.B = 13/28
B = 13/28 : 1/7
B = 13/28 . 7
B = 13/4
NH
1