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30 tháng 4 2018
\(\frac{4}{3}B=-1+\frac{3}{4}-\left(\frac{3}{4}\right)^2+...+\left(\frac{3}{4}\right)^{99}\)
\(B=-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{100}\)
\(\Rightarrow\)\(\frac{7}{3}B=-1+\left(\frac{3}{4}\right)^{100}\Rightarrow B=\frac{\left(\frac{3}{4}\right)^{100}-1}{\frac{7}{3}}=\frac{3\left[\left(\frac{3}{4}\right)^{100}-1\right]}{7}\)
Như vầy đủ gọn chưa bạn?
AK
1
9 tháng 8 2018
= (-0,37 +1,75) . (-1,1) - (2,63 - 0,375) . ( -1,1)
= 1,38 . ( -1,1) - 1,88 . (-1,1)
=-1,1 . ( 1,38 - 1,88 )
= -1,1 . ( -0,5)
=0,55
k mik nha
9 tháng 8 2018
\(=\left(-0,37+\frac{14}{8}\right).\left(-1.1\right)-\left(2,63-\frac{9}{24}\right).\left(-1,1\right)\)
\(=-1,1.\left(-0,37+\frac{14}{8}-2,63+\frac{9}{24}\right)\)
\(=-1,1.\left[\left(-0,37-2,63\right)+\left(\frac{14}{8}+\frac{9}{24}\right)\right]\)
\(=-1,1.\left[\left(-3\right)+\left(\frac{14}{8}+\frac{3}{8}\right)\right]\)
\(=-1,1.\left(-3+\frac{17}{8}\right)\)
\(=-1,1.\left(-\frac{7}{8}\right)\)
\(=\frac{77}{80}\)
S
25 tháng 4 2017
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(A=\frac{1-\frac{1}{3^{100}}}{2}\)
\(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(3B=\frac{5.3}{4.7}+\frac{5.3}{7.10}+\frac{5.3}{10.13}+...+\frac{5.3}{25.28}\)
\(3B=5\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(3B=5\cdot\frac{3}{14}=\frac{15}{14}\)
\(B=\frac{15}{14}:3=\frac{5}{14}\)
25 tháng 4 2017
a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)
b) \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{5}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+\frac{5}{3}.\left(\frac{1}{10}-\frac{1}{13}\right)+...+\frac{5}{3}.\left(\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\frac{3}{14}\)
\(\Rightarrow B=\frac{5}{14}\)
KS
6
NY
3 tháng 5 2018
\(\left(-\frac{15}{22}\div-\frac{5}{11}\right)\cdot\frac{2}{3}\)
\(=\left(-\frac{15}{22}\cdot-\frac{11}{5}\right)\cdot\frac{2}{3}\)
\(=-\frac{3}{2}\cdot\frac{2}{3}\)
\(=-1\)
O2
4
26 tháng 4 2018
B= 0,5 .4/3 .(-10) .0,75 .7/-35
B= 1/2 .4/3 .(-10) .3/4 .(-1)/5
B= [1/2 .(-1)/5 .(-10) ] .(4/3 .3/4)
B= 1 .1
B= 1
LN
6 tháng 7 2018
1+4+7+10+...+49+52+55+58-410
=[(58-1):3+1].(1+58):2-410
=20.59:2-410
=59.10-410
=590-410
=180
chúc bạn học tốt nha
=90 nha
100-10=90 k mình nha.