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NQ
3
HH
24 tháng 4 2017
A= \(\frac{5}{3}\)(\(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...\frac{3}{123.126}\)
A=\(\frac{5}{3}\)(\(\frac{1}{18}-\frac{1}{126}\))
A=\(\frac{5}{3}.\frac{1}{21}\)
A=\(\frac{5}{63}\)
24 tháng 4 2017
\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{4}{123.126}\)
\(=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(=\frac{5}{3}.\frac{1}{21}\)
\(=\frac{5}{63}\)
MM
1
1 tháng 4 2016
3/5*A=3/(18*21)+3/(21*24)+3/(24*27)+...+3/(123*126)
=>3/5*A=1/18-1/21+1/21-1/24+1/24-1/27+...+1/123-1/126
=>3/5*A=1/18-1/126
=>3/5*A=1/21
=>A=5/63
1 tháng 4 2016
A=\(\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+..........+\frac{3}{123.126}\right)\)
A=\(\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+............+\frac{1}{123}-\frac{1}{126}\right)\)
=\(\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
=\(\frac{5}{3}.\frac{1}{21}\)
=\(\frac{5}{63}\)
26 tháng 3 2017
\(A=\dfrac{25}{18\cdot21}+\dfrac{25}{21\cdot24}+\dfrac{25}{24\cdot27}+...+\dfrac{25}{123\cdot126}\)
\(=25\left(\dfrac{1}{18\cdot21}+\dfrac{1}{21\cdot24}+\dfrac{1}{24\cdot27}+...+\dfrac{1}{123\cdot126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{3}{18\cdot21}+\dfrac{3}{21\cdot24}+\dfrac{3}{24\cdot27}+...+\dfrac{3}{123\cdot126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)\(=\dfrac{25}{3}\cdot\dfrac{1}{21}=\dfrac{25}{63}\)
MN
26 tháng 3 2017
A= \(\dfrac{25}{18}-\dfrac{25}{21}+\dfrac{25}{21}-\dfrac{25}{24}+...+\dfrac{25}{123}-\dfrac{25}{126}\)
A= \(\dfrac{25}{18}-\dfrac{25}{126}\)
A= \(\dfrac{25}{21}\)
Hoặc ngay dòng 2 bạn làm như thế này cũng được: \(25.\left(\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)
C
1
30 tháng 3 2017
Đề sai. câu đầu phải là \(\dfrac{1}{18.21}\) mới đúng.
Nếu câu đầu là \(\dfrac{1}{18.21}\) thì mik có cách làm sau :
\(\dfrac{1}{18.21}+\dfrac{1}{21.24}+\dfrac{1}{24.27}+...+\dfrac{1}{123.126}\)
= \(\dfrac{1}{3}.\left(\dfrac{3}{18.21}+\dfrac{3}{21.24}+\dfrac{3}{24.27}+...+\dfrac{3}{123.126}\right)\)
= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{27}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)
= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)
= \(\dfrac{1}{3}.\dfrac{1}{21}\)
= \(\dfrac{1}{63}\)
31 tháng 1 2019
1,
\(\dfrac{3}{2^2}\cdot\dfrac{8}{3^2}\cdot\dfrac{15}{4^2}...\dfrac{899}{30^2}\\ =\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}....\dfrac{29\cdot31}{30\cdot30}\\ =\left(\dfrac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot....\cdot30}\right)\cdot\left(\dfrac{3\cdot4\cdot5\cdot....\cdot31}{2\cdot3\cdot4.....\cdot30}\right)\\ =\dfrac{1}{30}\cdot\dfrac{31}{2}\\ =\dfrac{31}{60}\)
2,
\(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{37\cdot38\cdot39}\\ =\dfrac{1}{2}\left(\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{37\cdot38\cdot39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+....+\dfrac{1}{37\cdot38}-\dfrac{1}{38\cdot39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{38\cdot39}\right)\\ =\dfrac{1}{4}-\dfrac{1}{3964}\\ =\dfrac{185}{741}\)
3, Làm tương tự, áp dụng ; \(\dfrac{n}{x\left(x+n\right)}=\dfrac{1}{x}-\dfrac{1}{x+n}\)
LN
2
21 tháng 2 2016
=> A = 6/3.( 1/15 - 1/18 + 1/18 - 1/21 + ..... + 1/87 - 1/90 )
=> A = 2.( 1/15 - 1/90 )
=> A = 2.5/90
=> A = 10/90 = 1/9
YN
4 tháng 6 2021
\(\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
\(\rightarrow\frac{6}{3}.\left(\frac{3}{15.18}+\frac{3}{18.21}+...+\frac{3}{87.90}\right)\)
\(\rightarrow2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(\rightarrow2.\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(\rightarrow\frac{1}{9}\)
29 tháng 3 2016
A = 6/3 . ( 1/15.18 + 1/18.21 + 1/21/24 + . . . + 1/87.90 )
A = 6/3 . ( 1/15 - 1/18 + 1/18 - 1/21 + 1/21 - 1/24 + . . . + 1/87 - 1/90 )
A = 2 . ( 1/15 - 1/90 )
A = 2. 5/90
A = 10/90 = 1/9
29 tháng 3 2016
\(\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{84.87}+\frac{6}{87.90}\)
\(=\frac{6}{3}\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{84.87}+\frac{3}{87.90}\right)\)
\(=2\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{84}-\frac{1}{87}+\frac{1}{87}-\frac{1}{90}\right)\)
\(=2\left(\frac{1}{15}-\frac{1}{90}\right)=2\left(\frac{6-1}{90}\right)=2\times\frac{1}{18}=\frac{1}{9}\)
\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)
\(A=\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(A=\frac{5}{3}.\frac{1}{21}\)
\(A=\frac{5}{63}\)