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S = 1.4 + 4.7 + 7.10 + 10.13 + ... + 61.64
1.4.9 = 1.4.(7 + 2) = 1.4.7 + 1.4.2
4.7.9 = 4.7.(10 - 1) = 4.7.10 - 1.4.7
7.10.9 = 7.10.(13 - 4) = 7.10.13 - 4.7.10
10.13.9 = 10.13.(16 - 7) = 10.13.16 - 7.10.13
.......................................................................
61.64.9 = 61.64.(67 - 58) = 61.64.67 - 58.61.64
Cộng vế với vế ta có:
1.4.9 + 4.7.9 + 7.10.9 +...+ 61.64.9 = 1.4.2 + 61.64.67
9(1.4 + 4.7 + 7.10+ ...+ 61.64) = 261576
1.4 + 4.7 + 7.10 +...+ 61.64 = 261576 : 9
1.4 + 4.7 + 7.10 + ... + 61.64 = 29064
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3/1.4+3/4.7+3/7.10+3/10.13
=1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13
=1 - 1/13
=12/13
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\(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}\)
\(=\dfrac{3\cdot1}{1\cdot4}+\dfrac{3\cdot1}{4\cdot7}+\dfrac{3\cdot1}{7\cdot10}+\dfrac{3\cdot1}{10\cdot13}+\dfrac{3\cdot3}{13\cdot16}\)
\(=3\cdot\left(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+\dfrac{1}{10\cdot13}+\dfrac{1}{13\cdot16}\right)\)
\(=3\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)
\(=3\cdot\left(1-\dfrac{1}{16}\right)\)
\(=3\cdot\left(\dfrac{16}{16}-\dfrac{1}{16}\right)\)
\(=3\cdot\dfrac{15}{16}\)
\(=\dfrac{45}{16}\)
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3/1.4 + 3/4.7 + .. +3/13.16
= 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16
= 1/1 - 1/16
= 15/16
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x/1.4+x/4.7+x/7.10+x/10.13+x/13.16=5/2
=>x/3(1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)=5/2
=>x/3.(1/4-1/16)=5/2
=>x/3.3/16=5/2
=>x/3=5/2:3/16
=>x/3=40/3
=>x=40
Vậy x=40
x/1.4 + x/4.7 + x/7.10 + x/10.13 + x/13.16 = 5/6
=> x.1/3.(3/1.4 + 3/4.7 + 3/7.10 + 3/10.13 + 3/13.16) = 5/6
=> x.1/3.(1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16) = 5/6
=> x.1/3.(1 - 1/16) = 5/6
=> x.1/3.15/16 = 5/6
=> x.1/3 = 5/6 : 15/16
=> x.1/3 = 8/9
=> x = 8/9 : 1/3
=> x = 8/3
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a) 1x( 1+3) ; 4x( 4+3) ; 7 x ( 7+3) ; 10 x ( 10 +3) ; ,,,,,,,,
b)1720
st1 = 1.4 = [ 3.(1-1) + 1].[3.(1-1) + 4]
st2 = 4.7 = [3.(2-1) + 1].[3.(2-1) + 4]
st3 = 7.10 = [3.(3-1) + 1].[3.(3-1) + 4]
..........................................................
stn = [3.(n - 1) + 1].(3.(n - 1) + 4]
stn = (3n - 2).(3n + 1)
số hạng thứ 15 của dãy số trên là:
(3.15 - 2).(3.15 + 1) = 43.46 = 1978
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ta nhân 3 cả hai vế, được :
\(\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{102.105}\right)x=3\)
hay
\(\left(\frac{4-1}{1.3}+\frac{7-4}{4.7}+...+\frac{105-102}{102.105}\right)x=3\) \(\Leftrightarrow\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+..+\frac{1}{102}-\frac{1}{105}\right)x=3\)
\(\Leftrightarrow\left(1-\frac{1}{105}\right)x=3\Leftrightarrow\frac{104}{105}.x=3\Leftrightarrow x=\frac{315}{104}\)
hình như bị sai đề thì phải
khong sai dau nhe