1/1+2 +1/2+3 +1/3+4 +1/4+5 .....1/13+14 = ?
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3 tháng 8 2015
a, \(\frac{-3}{7}+\frac{5}{13}-\frac{4}{7}+\frac{8}{13}\)
\(=\frac{-3}{7}-\frac{4}{7}+\frac{5}{13}+\frac{8}{13}\)
\(=-\frac{7}{7}+\frac{13}{13}=-1+1=0\)
b, \(\frac{-5}{14}-\frac{2}{-14}+\frac{1}{8}+\frac{1}{8}\)
\(=\frac{-5}{14}+\frac{2}{14}+\frac{1}{8}+\frac{1}{8}\)
\(=-\frac{3}{14}+\frac{1}{4}=\frac{1}{28}\)
c,\(-\frac{5}{13}-\left(\frac{3}{5}+\frac{3}{13}-\frac{4}{10}\right)\)
\(=-\frac{5}{13}-\frac{3}{13}-\frac{3}{5}+\frac{4}{10}\)
\(=-\frac{8}{13}-\frac{3}{5}+\frac{4}{10}=-\frac{79}{65}+\frac{4}{10}=-\frac{53}{65}\)
d, \(\left[\left(\frac{1}{8}-\frac{9}{7}+\frac{4}{6}-\frac{12}{7}-\frac{1}{2}\right)+\frac{5}{9}\right]\)
\(=\left[\left(\frac{1}{8}-\frac{9}{7}+\frac{2}{3}-\frac{12}{7}-\frac{1}{2}\right)+\frac{5}{9}\right]\)
\(=\left[\left(\frac{1}{8}-\frac{1}{2}-\frac{9}{7}-\frac{12}{7}+\frac{2}{3}\right)+\frac{5}{9}\right]\)
\(=-\frac{65}{24}+\frac{5}{9}=-2\frac{11}{72}\)
8 tháng 4 2017
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{13.14}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{13}-\dfrac{1}{14}\)
\(=\dfrac{1}{1}-\dfrac{1}{14}=\dfrac{13}{14}\)
Ta thấy: \(\dfrac{13}{14}< 1\)
Vậy A<1
LN
18 tháng 9 2018
a,=\(\dfrac{8}{14}-\dfrac{1}{14}+\dfrac{5}{21}+\dfrac{3}{2}\)
=\(\dfrac{1}{2}+\dfrac{3}{2}+\dfrac{5}{21}\) =\(2+\dfrac{5}{21}\) =\(\dfrac{42}{21}+\dfrac{5}{21}\) =\(\dfrac{47}{21}\)
b,=\(\dfrac{11}{13}.\dfrac{12}{15}-\dfrac{7}{15}+\dfrac{14}{15}.\dfrac{11}{13}\)
=\(\dfrac{11}{13}.\left(\dfrac{12}{15}+\dfrac{14}{15}\right)-\dfrac{7}{15}\)
=\(\dfrac{11}{13}.\dfrac{26}{15}-\dfrac{17}{15}\) =\(\dfrac{22}{15}-\dfrac{17}{15}\) =\(\dfrac{5}{15}\) =\(\dfrac{1}{3}\)
c,=\(\left(\dfrac{3}{6}-\dfrac{2}{6}\right)^2\) =\(\left(\dfrac{1}{6}\right)^2\) =\(\dfrac{1}{36}\)
d,=câu này dễ mà
DT
Đỗ Thanh Hải
CTVVIP
11 tháng 3 2021
a) \(\dfrac{\dfrac{3}{14}-\dfrac{3}{17}+\dfrac{3}{19}}{\dfrac{5}{19}+\dfrac{5}{14}-\dfrac{5}{17}}=\dfrac{3\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}{5\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}=\dfrac{3}{5}\)
DT
Đỗ Thanh Hải
CTVVIP
11 tháng 3 2021
c) \(\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{193}}{\dfrac{3}{7}+\dfrac{3}{5}+\dfrac{3}{17}-\dfrac{3}{293}}=\dfrac{2\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}{3\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}=\dfrac{2}{3}\)
d)
CM
23 tháng 7 2018
Lời giải chi tiết:
| 13 + 2 – 1 = 14 | 15 + 3 – 2 = 16 |
| 14 – 1 + 3 = 16 | 17 – 4 + 5 = 18 |
| 19 – 5 – 1 = 13 | 18 – 2 – 2 = 14 |
24 tháng 8 2023
Lời giải :
13 + 2 - 1 = 14 15 + 3 - 2 = 16
14 - 1 + 3 = 16 17 - 4 + 5 = 18
19 - 5 - 1 = 13 18 - 2 - 2 = 14
Chúc bạn học tốt ~_~
\(\frac{1}{1+2}+\frac{1}{2+3}+\frac{1}{3+4}+...+\frac{1}{13+14}=\frac{1}{2.3:2}+\frac{1}{3.4:2}+\frac{1}{4.5:2}+...+\frac{1}{14.15:2}=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{14.15}\)\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{14.15}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{14}-\frac{1}{15}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{15}\right)=\frac{1}{2}.2-\frac{1}{15}.2=1-\frac{2}{15}=\frac{13}{15}\)