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DP
16 tháng 7 2017
\(M=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+....+\frac{5}{46.51}\)
\(M=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+...+\frac{51-46}{46.51}\)
\(M=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{46}-\frac{1}{51}\)
\(M=1-\frac{1}{51}=\frac{50}{51}\)
\(N=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{199\cdot201}\)
\(N=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{199}-\frac{1}{201}\right)\)
\(N=\frac{1}{2}\cdot\left(1-\frac{1}{201}\right)\)
\(N=\frac{1}{2}\cdot\frac{200}{201}=\frac{100}{201}\)
29 tháng 6 2017
a) \(\frac{51}{3}-\frac{22}{3}=\frac{51-22}{3}=\frac{29}{3}\)
b) \(\frac{5}{12}+\frac{5}{6}-\frac{3}{4}=\frac{5}{12}+\frac{10}{12}-\frac{9}{12}=\frac{5+10-9}{12}=\frac{6}{12}=\frac{1}{2}\)
c) \(1-\left(\frac{1}{5}+\frac{1}{2}\right)=\frac{10}{10}-\frac{2}{10}-\frac{5}{10}=\frac{10-5-2}{10}=\frac{3}{10}\)
d) \(\frac{111}{4}-\left(\frac{25}{7}+\frac{51}{4}\right)=\frac{777}{28}-\frac{60}{28}-\frac{357}{28}=\frac{360}{28}=\frac{90}{7}\)
e) \(\left(\frac{85}{11}+\frac{35}{7}\right)-\frac{35}{11}=\left(\frac{85}{11}-\frac{35}{11}\right)+\frac{35}{7}=\frac{50}{11}-\frac{35}{7}=\frac{350}{77}-\frac{385}{77}=-\frac{35}{77}\)
NA
0
BH
10 tháng 6 2015
1> a) \(\frac{5}{7}x4:\frac{5}{9}=\frac{5}{7}:\frac{5}{9}x4=\frac{5}{7}x\frac{9}{5}x4=\frac{9}{7}x4=\frac{9x4}{7}=\frac{36}{7}\)
\(b,8x\frac{2}{3}:\frac{1}{2}=8x\frac{2}{3}x\frac{2}{1}=8x2x\frac{2}{3}=16x\frac{2}{3}=\frac{32}{3}\)
\(c,6:\frac{3}{5}-\frac{7}{6}x\frac{6}{7}=6x\frac{5}{3}-1=10-1=9\)
\(\frac{21}{5}x\frac{10}{11}+\frac{57}{11}=\frac{42}{11}+\frac{57}{11}=\frac{99}{11}=9\)
2) a) \(\frac{35}{9}:x=\frac{35}{6}\)
\(x=\frac{35}{9}:\frac{35}{6}\)
\(x=\frac{35}{9}x\frac{6}{35}\)
\(x=\frac{2}{3}\)
b) \(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)x10-X=0\)
\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{5}-\frac{1}{6}\right)x10-X=0\)
\(\left(\frac{1}{1}-\frac{1}{6}\right)x10-X=10\)
\(\frac{5}{6}x10-X=0\)
\(X=\frac{5}{6}x10=\frac{25}{3}\)
Đúng nha !!!!
10 tháng 6 2015
1/a/\(\frac{5}{7}\cdot4:\frac{5}{9}=\frac{20}{7}:\frac{5}{9}=\frac{20}{7}\cdot\frac{9}{5}=\frac{36}{7}\)
b/\(8\cdot\frac{2}{3}:\frac{1}{2}=\frac{16}{3}:\frac{1}{2}=\frac{16}{3}\cdot\frac{2}{1}=\frac{32}{3}\)
c/\(6:\frac{3}{5}-\frac{7}{6}\cdot\frac{6}{7}=6\cdot\frac{5}{3}-1=10-1=9\)
2/a/\(\frac{35}{9}:x=\frac{35}{6}\)
\(x=\frac{35}{9}:\frac{35}{6}=\frac{35}{9}\cdot\frac{6}{35}\)
\(x=\frac{2}{3}\)
b/\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\right)\cdot10-x=0\)
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\cdot10-x=0\)
\(\left(\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{2}{30}\right)\cdot10-x=0\)
\(\frac{47}{60}\cdot10-x=0\)
\(\frac{47}{6}-x=0\)
\(x=\frac{47}{6}-0\)
\(x=\frac{47}{6}\)
PQ
1
T
1 tháng 6 2019
#)Giải :
\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-\frac{19}{45}+...-\frac{119}{4950}\)
\(S=\frac{38}{25}+\left(\frac{9}{10}-\frac{11}{15}\right)+\left(\frac{13}{21}-\frac{15}{28}\right) +\left(\frac{17}{36}-\frac{19}{45}\right)+...+\left(\frac{197}{4851}-\frac{199}{4950}\right)\)
Ta thấy :
\(\left(\frac{9}{10}-\frac{11}{15}\right)=\frac{1}{6}=\frac{1}{\left(2.3\right)}=\frac{1}{2}-\frac{1}{3}\)
\(\left(\frac{13}{21}-\frac{15}{28}\right)=\frac{1}{12}=\frac{1}{\left(3.4\right)}=\frac{1}{3}-\frac{1}{4}\)
\(\left(\frac{17}{36}-\frac{19}{45}\right)=\frac{1}{20}=\frac{1}{\left(4.5\right)}=\frac{1}{4}-\frac{1}{5}\)
..........................................................
\(\left(\frac{197}{4851}-\frac{199}{4950}\right)=\frac{1}{2450}=\frac{1}{\left(49.50\right)}=\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow S=\frac{38}{25}+\left[\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\right]\)
\(\Rightarrow S=\frac{38}{25}+\left[\frac{1}{2}-\frac{1}{50}\right]\)
\(\Rightarrow S=\frac{38}{25}+\frac{24}{50}\)
\(\Rightarrow S=2\)
#~Will~be~Pens~#
10 tháng 8 2018
a) (44 x 52 x 60) : (11 x 13 x 15)
= (44 : 11) x ( 52 : 13) x (60 : 15)
= 4 x 4 x 4 = 64
d) 1 + 6 + 11 + 16 + ... + 46 + 51
Ta có : 1 + 6 + 11 + 16 + ... + 46 + 51 ( có 11 số )
= (51 + 1) x 11 : 2 = 286
2 tháng 8 2020
a) SSH : (101 - 2) : 1 + 1 = 100
=> Tổng : \(\frac{\left(2+101\right)\cdot100}{2}=5150\)
b) SSH : (201 - 101) : 2 + 1 = 51
=> Tổng : \(\frac{\left(101+201\right)\cdot51}{2}=7701\)
c) SSH : (293 - 5) : 3 + 1 = 97
=> Tổng : \(\frac{\left(5+293\right)\cdot97}{2}=14453\)
P/S : Đề bài là gì ?? '-'