Tính A=1/1.6+1/3.10+1/5.14+....+1/41.86
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MD
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
30 tháng 6 2020
\(A=\frac{1}{1.2.3}+\frac{1}{3.2.5}+\frac{1}{5.2.7}+\frac{1}{7.2.9}+...+\frac{1}{41.2.43}\)
\(4A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{41.43}\)
\(4A=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{43-41}{41.43}\)
\(4A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{41}-\frac{1}{43}=1-\frac{1}{43}\)
\(A=\frac{1}{4}-\frac{1}{172}=\frac{42}{172}=\frac{21}{86}\)
LP
0
28 tháng 3 2018
Ta có: *)A.5=5(1/3.8+1/8.13+...+1/33.38)
=5/3.8+5/8.13+...+5/33.38
=1/3-1/8+1/8-1/13+...+1/33-1/38
=1/3-1/38
=> A=(1/3-1/38).1/5
*)7B=7/3.10+7/10.17+7/17.24+...+7/31.38
=1/3-1/10+1/10-1/17+...+1/31-1/38
=1/3-1/38
=>B=(1/3-1/38).1/7
Do đó a/b=(1/5)/(1/7)=7/5
k mk nha!
DN
2
1 tháng 8 2015
5A = 5/3.8 + 5/8.13 + 5/13.18 + ... + 5/33.38
= 1/3 - 1/8 + 1/8 - 1/13 + ... + 1/33 - 1/38
= 1/3 - 1/38
5A = 35/114
=> A = 35/114 : 5 = 7/144
7B = 7/3.10 + 7/10.17 + ... + 7/31.38
= 1/3 - 1/10 + 1/10- 1/17 + .. + 1/31 - 1/38
= 1/3 - 1/38
B = 35/144 : 7 = 5/144
VẬy A> B
PE
1
1 tháng 8 2015
A=1/3.8+1/8.13+1/13.18+...+1/33.38
5A=5/3.8+5/8.13+5/13.18+...+5/33.38
5A=1/3-1/8+1/8-1/13+1/13-1/18+...+1/33-1/38
5A=1/3-1/38
5A=38/114-3/114
5A=35/114
A=35/114:5
A=7/114
B=1/3.10+1/10.17+1/17.24+1/24.31+1/31.38
7B=7/3.10+7/10.17+7/17.24+7/24.31+7/31.38
7B=1/3-1/10+1/0-1/17+1/17-1/24+1/24-1/31+1/31-1/38
7B=1/3-1/38
7B=38/114-3/114
7B=35/114
B=35/114:7
B=5/114
BT
1
T
6 tháng 10 2023
\(A=\dfrac{1}{1\cdot6}-\dfrac{1}{6\cdot11}-\dfrac{1}{11\cdot16}-\dfrac{1}{16\cdot21}-...-\dfrac{1}{46\cdot51}\)
\(=\dfrac{1}{6}-\left(\dfrac{1}{6\cdot11}+\dfrac{1}{11\cdot16}+\dfrac{1}{16\cdot21}+...+\dfrac{1}{46\cdot51}\right)\)
\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{46\cdot51}\right)\)
\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{46}-\dfrac{1}{51}\right)\)
\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{51}\right)\)
\(=\dfrac{1}{6}-\dfrac{1}{5}\cdot\dfrac{5}{34}\)
\(=\dfrac{1}{6}-\dfrac{1}{34}\)
\(=\dfrac{7}{51}\)
Vậy \(A=\dfrac{7}{51}\)
VT
2
TQ
23 tháng 9 2015
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+.........+\frac{1}{3^{100}}\)
\(\Rightarrow3A-A=1+\frac{1}{3}+\frac{1}{3^2}+.........+\frac{1}{3^{100}}-\left(\frac{1}{3}+\frac{1}{3^2}+.......+\frac{1}{3^{99}}\right)=1+\frac{1}{3}\)
\(\Rightarrow2A=1+\frac{1}{3}\Rightarrow A=\left(1+\frac{1}{3}\right):2\)
23 tháng 9 2015
=>3A=1/3^2+1/3^3+1/3^4+...+1/3^100
=>3A-A=(1/3^2+1/3^3+1/3^4+...+1/3^100) - (1/3+1/3^2+1/3^3+...+1/3^99)
=>2A=1/3^100-1/3
=>A=(\(\frac{1}{3^{100}}\)- \(\frac{1}{3}\)):2
Li ke mình nha!
BM
3
20 tháng 4 2018
\(A=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}\right):5\)
\(A=\left(1-\frac{1}{501}\right):5\)
\(A=\frac{500}{501}:5=\frac{100}{501}\)
20 tháng 4 2018
Ta có : \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right) \)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(\Rightarrow\) \(A=\frac{1}{5}.\frac{501-1}{501}=\frac{1}{5}.\frac{500}{501}\)
\(\Rightarrow\) \(A=\frac{1.500}{5.501}=\frac{20}{1.501}=\frac{20}{501}\)
Vậy \(A=\frac{20}{501}\)
A=1/1.6+1/3.10+1/5.14+..........+1/41.86
A=1/2(1/1.3+1/3.5+1/5.7+.............+1/41.43)
A=1/2(1-1/3+1/3-1/5+1/5-1/7+..............+1/41-1/43)
A=1/2(1-1/43)
A=1/2*42/43=21/43
HỌC TỐT NHÉ!!!
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