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\(-3\dfrac{1}{7}:\left\{\left[2+1\dfrac{3}{5}:\left(\dfrac{4}{3}-1,6\right)\right]+25\%\right\}\)
\(=-\dfrac{22}{7}:\left\{\left[2+\dfrac{8}{5}:\left(\dfrac{4}{3}-\dfrac{8}{5}\right)\right]+\dfrac{1}{4}\right\}\)
\(=-\dfrac{22}{7}:\left[\left(2+\dfrac{8}{5}:\left(-\dfrac{4}{15}\right)\right)+\dfrac{1}{4}\right]\)
\(=-\dfrac{22}{7}:\left(2-6+\dfrac{1}{4}\right)\)
\(=-\dfrac{22}{7}:\left(-\dfrac{15}{4}\right)\)
\(=-\dfrac{22}{7}.\dfrac{-4}{15}\)
\(=\dfrac{88}{105}\)
\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{997.999}\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{997.999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{997}-\frac{1}{999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(1-\frac{1}{999}\right)=\frac{5}{2}.\frac{998}{999}=\frac{2495}{999}=2\frac{497}{999}\)
\(A=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}\)
\(\Leftrightarrow A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(1-\frac{1}{16}\right)=\frac{2}{3}.\frac{15}{16}=\frac{5}{8}\)
C = 5/1x3 + 5/3x5 + 5/5x7 + ... + 5/997x999
C = 5 - 5/3 + 5/3 - 5/5 + 5/5 - 5/7 + ... + 5/997 - 5/999
C = 5 - 5/999
C = bạn tự tính nhé !
A = 2/4 + 2/28 + 2/70 + 2/130 + 2/208
A = 2/1x4 + 2/4x7 + 2/7x10 + 2/10x13 + 2/13x16
A = 2 - 2/4 + 2/4 - 2/7 + 2/7 - 2/10 + 2/10 - 2/13 + 2/13 - 2/16
A = 2 - 2/16
A = bạn tự tính nhé !
a, 11 + 112 + 113 + ... + 117 + 118
= (11 + 112) + (113 + 114) + ... + (117 + 118)
= 11(1 + 11) + 113(1 + 11) + ... + 117(1 + 11)
= 11.12 + 113.12 + .... + 117.12
= 12(11 + 113 + ... + 117) chia hết cho 12
b, 7 + 72 + 73 + 74
= (7 + 73) + (72 + 74)
= 7(1 + 72) + 72(1 + 72)
= 7.50 + 72.50
= 50(7 + 72) chia hết cho 50
c, 3 + 32 + 33 + 34 + 35 + 36
= (3 + 32 + 33) + (34 + 35 + 36)
= 3(1 + 3 + 32) + 34(1 + 3 + 32)
= 3.13 + 34.13
= 13(3 + 34) chia hết cho 13
Vì (n+7) chia hết cho (n+5)
Nên [(n+5)+2] chia hết cho (n+5)
Mà (n+5) chia hết cho (n+5)
Suy ra, 2 chia hết cho (n+5)
Suy ra,(n+5) là Ư(2)
Ư(2)={-2;-1;1;2}
Vậy tập hợp các giá trị n là { -7;-6;-4;-3}
a) \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+........+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.........+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
b) \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+..........+\frac{2}{73.75}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{73}-\frac{1}{75}\)
\(=\frac{1}{3}-\frac{1}{75}=\frac{8}{25}\)
c) \(\frac{4}{4.6}+\frac{4}{6.8}+\frac{4}{8.10}+..........+\frac{4}{64.66}\)
\(=2.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+..........+\frac{2}{64.66}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+.....+\frac{1}{64}-\frac{1}{66}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{66}\right)=2.\frac{31}{132}=\frac{31}{66}\)
d) \(\frac{9}{5.8}+\frac{9}{8.11}+\frac{9}{11.14}+........+\frac{9}{497.500}\)
\(=3.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+..........+\frac{3}{497.500}\right)\)
\(=3.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+......+\frac{1}{497}-\frac{1}{500}\right)\)
\(=3.\left(\frac{1}{5}-\frac{1}{500}\right)=3.\frac{99}{500}=\frac{297}{500}\)
e) \(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+......+\frac{1}{93.95}\)
\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+........+\frac{2}{93.95}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+........+\frac{1}{93}-\frac{1}{95}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{95}\right)=\frac{1}{2}.\frac{18}{95}=\frac{9}{95}\)
g) \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+..........+\frac{1}{200.203}\)
\(=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+........+\frac{3}{200.203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+......+\frac{1}{200}-\frac{1}{203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{203}\right)=\frac{1}{3}.\frac{201}{406}=\frac{67}{406}\)
\(\frac{4}{7}+\frac{3}{4}+\frac{2}{7}+\frac{5}{4}+\frac{1}{7}\)
\(=\left(\frac{4}{7}+\frac{2}{7}+\frac{1}{7}\right)+\left(\frac{3}{4}+\frac{5}{4}\right)\)
\(=\frac{7}{7}+\frac{8}{4}\)
\(=1+2\)
\(=3\)
4/7+3/4+2/7+5/4+1/7
=( 4/7 + 1/7 + 2/7 )+(3/4+5/4 )
= 1 + 2
= 3
k mk nhé