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\(=5\cdot3\cdot\dfrac{7}{10}=\dfrac{15}{10}\cdot7=\dfrac{3}{2}\cdot7=\dfrac{21}{2}\)
Ta có quy luật : 2 = 1.2 ; 6 = 2.3 ; 12 = 3.4 ; .......
Vậy số hạng thứ 100 của dãy số trên là 100.101 = 10100
\(\dfrac{5}{8}+\dfrac{7}{24}\) = \(\dfrac{15}{24}\) + \(\dfrac{7}{24}\) = \(\dfrac{22}{24}\) = \(\dfrac{11}{12}\)
\(\dfrac{6}{5}+\dfrac{9}{30}=\dfrac{36}{30}+\dfrac{9}{30}=\dfrac{45}{30}=\dfrac{3}{2}\)
\(\dfrac{7}{12}\) + \(\dfrac{5}{2}\) = \(\dfrac{7}{12}+\dfrac{30}{12}=\dfrac{37}{12}\)
\(\dfrac{9}{21}\) + \(\dfrac{6}{49}\) = \(\dfrac{3}{7}\) + \(\dfrac{6}{49}\) = \(\dfrac{21}{49}\) + \(\dfrac{6}{49}\) = \(\dfrac{27}{49}\)
b: 12/20+6/18=3/5+1/3=9/15+5/15=14/15
c: 8/12+20/30=2/3+2/3=4/3
d: 10/12+12/36=5/6+2/6=7/6
= 9 x ( 1/6 + 1/12 + 1/20 + 1/30 + 1/42 )
= 9 x (1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 )
= 9 x ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1 / 6 + 1 /6 - 1/7)
= 9x ( 1/2 - 1/7 )
= 9 x 5/14
= 45/14
Đề bài thiếu số hạng 3/20.
\(A=\dfrac{3}{2}+\dfrac{3}{6}+\dfrac{3}{12}+\dfrac{3}{20}+\dfrac{3}{30}+\dfrac{3}{42}\)
\(\dfrac{A}{3}=\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+\dfrac{1}{5x6}+\dfrac{1}{6x7}=\)
\(=\dfrac{2-1}{1x2}+\dfrac{3-2}{2x3}+\dfrac{4-3}{3x4}+...+\dfrac{7-6}{6x7}=\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{6}-\dfrac{1}{7}=\)
\(=1-\dfrac{1}{7}=\dfrac{6}{7}\Rightarrow A=3x\dfrac{6}{7}=\dfrac{18}{7}\)
12 : 30 = 0.4
6 : 30 = 0.2
HT
:)))
12 : 30 = 0,4
6 : 30 = 0,2
HT