Tính tổng sau:
A=5/15+5/35+5/63+....+5/399
K
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KL
6
8 tháng 6 2017
Ta có:
\(A=\frac{5}{15}+...+\frac{5}{399}\)
\(\Rightarrow A=5.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)
\(\Rightarrow A=\frac{5}{2}.\left(\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{5}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{5}{7}\)
AN
2
30 tháng 8 2015
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=\frac{5}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{11\cdot13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\frac{12}{13}\)
\(=\frac{30}{13}\)
30 tháng 8 2015
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}.\frac{12}{13}\)
\(=\frac{30}{13}\)
DT
22 tháng 4 2016
Ta có:
A=5/15+5/35+5/63+5/99+...+5/2915
=>A=5/3.5+5/5.7+5/7.9+5/9.11+...+5/53.55
=>A=5/2.(2/3.5+2/5.7+2/7.9+2/9.11+...+2/53.55)
=>A=5/2.(2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+...+2/53-2/55)
=>A=5/2.(2/3-2/55)
=>A=5/2.104/165
=>A=52/33
Vậy A=52/33
OK!
24 tháng 6 2016
Mk ko chép lại đầu bài đâu,thông cảm nha mk chỉ biết giải ý B
3B=1.2.3+2.3.3+3.4.3+...+1000.1001.3
=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+1000.1001.(1002-999)
=1.2.3-1.2.0+2.3.4-2.3.1+3.4.5-3.4.2+...+1000.1001.1002-1000.1001.999
=(1.2.3+2.3.4+3.4.5+...+1000.1001.1002) - (1.2.0+2.3.1+3.4.2+...+1000.1001.999)
=1000.1001.1002
=>B=(1000.1001.1002):3
=334 334 000
k hộ mk nha!
NN
4
MH
4 tháng 2 2016
\(y=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)
4 tháng 2 2016
mình thắc mắc quy luật của phép tính trên là gì : 15 -> 35 -> 63 ... -> 399 ?
20 tháng 2 2022
\(\frac{2}{15}+\frac{2}{35}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{2}{7}\)
HT
DV
1
26 tháng 5 2016
D =3-32-....-3100
(=)D=3-(32+33+....+3100)
(=)3D=3.3-(33+....+3101)
(=)2D=6-(3101-32)
(=)D=6-(3101-32) :2
B=-2/15-2/35-....-2/399
(=)B=-2/15-(2/35-...-2/399)
(=)B=-2/15-(2/5.7-...-2/19.21)
(=)B=-2/15-(1/5-1/21)
(=)B=-2/15-16/105
(=)B=-2/7
24 tháng 7 2019
\(A=5\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{6480}\right)\)
\(=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{80.81}\right)\)
\(=5\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{81-80}{80.81}\right)\)
\(=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{80}-\frac{1}{81}\right)\)
\(=5\left(1-\frac{1}{81}\right)=\frac{5.80}{81}=\frac{400}{81}\)
b)
\(B=7\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{483}\right)\)
\(=7.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{21.23}\right)\)
=> \(2.B=7\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{21.23}\right)\)
\(=7\left(\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{23-21}{21.23}\right)\)
\(=7.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{21}-\frac{1}{23}\right)\)
\(=7\left(\frac{1}{3}-\frac{1}{23}\right)=\frac{7.20}{69}=\frac{140}{69}\)
=> \(B=\frac{140}{69}:2=\frac{70}{69}\)
\(A=\frac{5}{3\cdot5}+\frac{5}{5\cdot7}+\frac{5}{7\cdot9}+......+\frac{5}{19\cdot21}\)
\(A=\frac{5}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{19}-\frac{1}{21}\right)\)
\(A=\frac{5}{2}\left(\frac{1}{3}-\frac{1}{21}\right)\)
còn lại tự tính nha
ok xong r đó
\(A=\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+...+\frac{5}{399}\)
\(A=\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+...+\frac{5}{19.21}\)
\(2A=5\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(2A=5.\frac{2}{7}\)
\(2A=\frac{10}{7}\)
\(\Rightarrow A=\frac{5}{7}\)