NH
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K
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NT
4
TY
3 tháng 3 2017
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{199.201}\).
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{199.201}\)
\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\)
\(2A=\frac{1}{1}-\frac{1}{201}\)
\(2A=\frac{201-1}{201}\)
\(2A=\frac{200}{201}\)
\(A=\frac{200}{201}:2\)
\(A=\frac{200}{402}\)
NH
3
18 tháng 3 2017
G=7/2.(2/1.3+2/3.5+2/5.7+...+2/199.201)
G=7/2.(1-1/3+1/3-1/5+1/5-1/7+.....+1/199.201
G=7/2.(1-1/201)
G=7/2.200/201
G=1400/402
G=700/201
TM
18 tháng 3 2017
\(G=\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{199.201}\)
\(G=7\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{199.200}\right)\)
\(G=\frac{7}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{199.201}\right)\)
\(G=\frac{7}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\right)\)
\(G=\frac{7}{2}\left(1-\frac{1}{201}\right)\)
\(G=\frac{7}{2}.\frac{200}{201}\)
\(G=\frac{700}{201}\)
DT
4
24 tháng 3 2017
M = 2 / 3.5 + 2 / 5.7 + 2 / 7.9 +...+2 / 97.99
M = 5 - 3 / 3 . 5 + 7 - 5 / 5 .7 + 9 - 7 / 7 . 9 +...+ 99 - 97 / 97 .99
M = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 -1/9 +...+ 1/97 - 1/99
M = 1/3 - 1/99
M = 33 /99 - 1/99
M = 32/99
vậy M= 32/99
HT
11
15 tháng 5 2015
Ta có: \(\frac{2}{3.5}=\frac{5-3}{3.5}=\frac{5}{3.5}-\frac{3}{3.5}=\frac{1}{3}-\frac{1}{5}\)
\(\frac{2}{5.7}=\frac{7-5}{5.7}=\frac{7}{5.7}-\frac{5}{5.7}=\frac{1}{5}-\frac{1}{7}\)
..................................................................
\(\frac{2}{97.99}=\frac{99-97}{97.99}=\frac{99}{97.99}-\frac{97}{97.99}=\frac{1}{97}-\frac{1}{99}\)
Vậy \(M=\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{95.97}+\frac{2}{97.99}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{3}-\left(\frac{1}{5}-\frac{1}{5}\right)-\left(\frac{1}{7}-\frac{1}{7}\right)-...-\left(\frac{1}{95}-\frac{1}{95}\right)-\left(\frac{1}{97}-\frac{1}{97}\right)-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
15 tháng 5 2015
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)
=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)
=\(\frac{1}{3}-\frac{1}{99}\)
=\(\frac{33}{99}-\frac{1}{99}\)
=\(\frac{23}{99}\)
LD
9 tháng 5 2018
S=1/3-1/5+1/5-1/7+........+1/2017-1/2019
S=1/3-1/2019
S=872/2019
DL
3
CT
23 tháng 3 2016
M = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ..... + 1/97 - 1/99
M = 1/3 - 1/99
M = 32/99
NT
2
11 tháng 4 2015
=3.(3/1.3+3/3.5+3/5.7+...+3/95.97+3/97.99)
=3(1-1/3+1/3-1/5+1/5-1/7+...+1/95-1/97+1/97-1/99)
=3[(1-1/99)+(1/5-1/5)+(1/7-1/7)+...+(1/97-1/97)]
=3(1-1/99)=3(99/99-1/99)=3.98/99=1.98/33=98/33
NH
13 tháng 4 2019
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
13 tháng 4 2019
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{97.99}\)
\(=\frac{2}{2}.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{97.99}\right)\)
\(=1.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=1.\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=1.\frac{33-1}{99}\)
\(=\frac{32}{99}\)
...................................TK CHO MK NHÉ.........................
PT
4
NH
17 tháng 6 2019
\(D=\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{199.201}\)
\(D=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{199.201}\right)\)
\(D=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{199}-\frac{1}{201}\right)\)
\(D=\frac{3}{2}\left(1-\frac{1}{201}\right)\)
\(D=\frac{3}{2}.\frac{200}{201}\)
\(D=\frac{100}{67}\)
T
17 tháng 6 2019
#)Giải :
\(D=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{199.201}\)
\(D=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{199.201}\right)\)
\(D=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\right)\)
\(D=\frac{3}{2}\left(1-\frac{1}{201}\right)\)
\(D=\frac{3}{2}\times\frac{200}{201}\)
\(D=\frac{100}{67}\)
ta có:
201.3 + 2/3.5+2/5.7+..................+2/199.201
= 201.3+ 2/2 . ( 1/3 -1/5)+2/2.(1/5-1/7)+2/2.(1/5-1/7) +..............+2/2.(1/199.1/201)
201.3 +2/2.1/3.-2/2.1/5+2/2.1/5-2/2.1/7..........................+2/2.1/199-2/2.1/201
=201.3 +2/2.(1/3+1/5-1/5+1/7-1/7.................+1/99.1/201)
=201.3+2/2.(1/3-1/201)
=201.3+22/67
=198
^-^