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NM
24 tháng 3 2019
a) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{14}{30}=\frac{7}{15}\)
LN
24 tháng 3 2019
a)
\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=2\left(1-\frac{1}{15}\right)\)
\(=2.\frac{14}{15}\)
\(=\frac{28}{15}\)
b)
\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)
\(...\)
LU
0
RK
2
Q
16 tháng 3 2018
Có: \(N=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
\(=>N=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(=>N=\frac{2}{4\cdot5}+\frac{2}{5\cdot6}+\frac{2}{6\cdot7}+...+\frac{2}{15\cdot16}\)
\(=>N=\left(\frac{2}{4}-\frac{2}{5}+\frac{2}{5}-\frac{2}{6}+...+\frac{2}{15}-\frac{2}{16}\right)\)
\(=>N=\frac{2}{4}-\frac{2}{16}\)
\(=>N=\frac{1}{2}-\frac{1}{8}\)
\(=>N=\frac{8-2}{16}=\frac{6}{16}=\frac{3}{8}\)
Vậy \(N=\frac{3}{8}\)
16 tháng 3 2018
Ta có :
\(N=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(N=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(N=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(N=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(N=2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(N=\frac{1}{2}-\frac{1}{8}\)
\(N=\frac{3}{8}\)
Vậy \(N=\frac{3}{8}\)
Chúc bạn học tốt ~
2 tháng 4 2017
21)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)
21 tháng 4 2018
A=1+(1/6+1/12+1/20+...+1/90):2
A=1+(1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10):2
A=1+(1/2-1/10):2
A=1+2/5:2
A=1+1/5
A=6/5
Vậy A=6/5 nha bạn
Đúng 100%
k mk nha
Mk nhanh nhất
PT
1
18 tháng 12 2015
B = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
\(B=\frac{1}{4.5:2}+\frac{1}{5.6:2}+\frac{1}{6.7:2}+.....+\frac{1}{15.16:2}\)
\(\frac{1}{2}B=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\)
Ta thấy: \(\frac{1}{4.5}=\frac{1}{4}-\frac{1}{5};\frac{1}{5.6}=\frac{1}{5}-\frac{1}{6};\frac{1}{6.7}=\frac{1}{6}-\frac{1}{7};.....\)
\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-.....-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)
\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{16}=\frac{3}{16}\)
\(B=\frac{3}{16}:\frac{1}{2}=\frac{3}{16}.2=\frac{3}{8}\)
22 tháng 3 2017
\(E=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)
\(E=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)
\(E=2\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)
\(E=2\left(\frac{1}{4x5}+\frac{1}{5x6}+...+\frac{1}{15x16}\right)\)
\(E=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(E=2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(E=\frac{3}{8}\)
22 tháng 3 2017
1/2E=1/20+1/30+1/42+...+1/240. =>1/2E=1/4*5+1/5*6+1/6*7+...+1/15*16. =>1/2E=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16. =>1/2E=1/4-1/16=3/16. =>E=3/16:1/2=3/8. Câu b có vấn đề.
AK
10 tháng 4 2018
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)
\(A=1-\frac{1}{6}\)
\(A=\frac{6}{6}-\frac{1}{6}\)
\(A=\frac{5}{6}\)
\(B=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)
\(B=2.\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)
\(B=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+..+\frac{1}{15.16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(B=2.\left(\frac{4}{16}-\frac{1}{16}\right)\)
\(B=2.\frac{3}{16}\)
\(B=\frac{3}{8}\)
Chúc bạn học tốt !!!
10 tháng 4 2018
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)
\(A=\frac{1}{1}-\frac{1}{6}\)
\(A=\frac{5}{6}\)
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(B=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(B=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(B=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(B=2.\frac{3}{16}\)
\(B=\frac{6}{16}=\frac{3}{13}\)
3 tháng 4 2019
=2/3.5/6.9/10.14/15.20/21.27/28
=5/9.21/15.45/49
=7/9.45/49
=5/7
hơi dài dòng nhưng mong bạn tích đúng cho mk nha