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\(\left(\dfrac{-1}{3}\right)^{-1}=-3\)
Vì \(\left(\dfrac{-1}{3}\right)^{-1}=\left(\dfrac{1}{-3}\right)^{-1}=\left(-3^{-1}\right)^{-1}=-3^{-1\times\left(-1\right)}=-3^1=-3\)
=> \(\left(\dfrac{-1}{3}\right)^{-1}=-3\)
A=1+3/2^3+4/2^4+5/2^5+...100/2^100
1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 + 100/2^101
A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101
= [1/2+1/2^2 +1/2^3 +...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3)
=[1-(1/2)^101]/(1-1/2) -100/2^101
=(2^101 -1)/2^100 - 100/2^101
=> A = (2^101 -1)/2^99 - 100/2^100
Bạn ơi khó hiểu quá bạn giải chi tiết hơn giúp mình nhé mình sẽ k cho bạn 2 cái nhé
a,
\(A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)...\left(1-\frac{1}{900}\right)\\ =\left(1-\frac{1}{2}\right)\left(1+\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1+\frac{1}{3}\right)...\left(1-\frac{1}{30}\right)\left(1+\frac{1}{30}\right)\\ =\frac{1}{2}\cdot\frac{3}{2}\cdot\frac{2}{3}\cdot\frac{4}{3}\cdot...\cdot\frac{29}{30}\cdot\frac{31}{30}\\ =\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{29}{30}\cdot\frac{3}{2}\cdot\frac{4}{3}\cdot...\cdot\frac{31}{30}\\ =\frac{1\cdot2\cdot...\cdot29}{2\cdot3\cdot...\cdot30}\cdot\frac{3\cdot4\cdot...\cdot31}{2\cdot3\cdot...\cdot30}\\ =\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)
b,
\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{98\cdot99\cdot100}\right)\\ =\frac{1}{2}\left(\frac{3-1}{1\cdot2\cdot3}+\frac{4-2}{2\cdot3\cdot4}+...+\frac{100-98}{98\cdot99\cdot100}\right)\\ =\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\right)\\ =\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)\\ =\frac{1}{2}\cdot\frac{4450-1}{9900}=\frac{1}{2}\cdot\frac{4449}{9900}=\frac{4449}{19800}=\frac{1483}{6600}\)
c, (Chịu :V)
d,
\(D=\frac{1}{3}\left(\frac{3}{1\cdot2\cdot3\cdot4}+\frac{3}{2\cdot3\cdot4\cdot5}+...+\frac{3}{27\cdot28\cdot29\cdot30}\right)\\ =\frac{1}{3}\left(\frac{4-1}{1\cdot2\cdot3\cdot4}+\frac{5-2}{2\cdot3\cdot4\cdot5}+...+\frac{30-27}{27\cdot28\cdot29\cdot30}\right)\\ =\frac{1}{3}\left(\frac{1}{1\cdot2\cdot3}-\frac{1}{2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4}-\frac{1}{3\cdot4\cdot5}+...+\frac{1}{27\cdot28\cdot29}-\frac{1}{28\cdot29\cdot30}\right)\\ =\frac{1}{3}\left(\frac{1}{6}-\frac{1}{24630}\right)\\ =\frac{228}{4105}\)
Chúc bạn học tốt nha
.
\(\dfrac{9^{15}.8^{11}}{3^{29}.16^8}=\dfrac{\left(3^2\right)^{15}.\left(2^3\right)^{11}}{3^{29}.\left(2^4\right)^8}=\dfrac{3^{30}.2^{33}}{3^{29}.2^{32}}\)
Ta lấy vễ trên chia vế dưới
\(=3.2=6\)
\(\dfrac{2^{11}.9^3}{3^5.16^2}=\dfrac{2^{11}.\left(3^2\right)^3}{3^5.\left(2^4\right)^2}=\dfrac{2^{11}.3^6}{3^5.2^8}\)
Ta lấy vế trên chia vế dưới
\(=2^3.3=24\)
\(\dfrac{9^{15}.8^{11}}{3^{29}.16^8}=\dfrac{\left(3^2\right)^{15}.\left(2^3\right)^{11}}{3^{29}.\left(2^4\right)^8}=\dfrac{3^{30}.2^{33}}{3^{29}.3^{32}}=3.2=6\)
\(\dfrac{2^{11}.9^3}{3^5.16^2}=\dfrac{2^{11}.\left(3^2\right)^3}{3^5.\left(2^4\right)^2}=\dfrac{2^{11}.3^6}{3^5.2^8}=2^3.3=8.3=24\)
a)×+1/ 53 + ×+2 /52 + ×+3/ 51+3 = 0
\(\Rightarrow\frac{x+1}{53}+1+\frac{x+2}{52}+1+\frac{x+3}{51}+1+\frac{3\left(x+54\right)}{\left(x+54\right)}=0\)
\(\Rightarrow\frac{x+54}{53}+\frac{x+54}{52}+\frac{x+54}{51}+\frac{x+54}{\frac{1}{3}\left(x+54\right)}=0\)
\(\Rightarrow\left(x+54\right)\left(\frac{1}{53}+\frac{1}{52}+\frac{1}{51}+\frac{1}{\frac{1}{3}\left(x+54\right)}\right)=0\)
\(\Rightarrow x+54=0\).Do \(\frac{1}{53}+\frac{1}{52}+\frac{1}{51}+\frac{1}{\frac{1}{3}\left(x+54\right)}\ne0\)
=>x=-54
b)×-2/ 72 + ×-3/ 71 + ×-4/ 70 -3 = 0
\(\Rightarrow\frac{x-2}{72}-1+\frac{x-3}{71}-1+\frac{x-4}{70}-1-\frac{3\left(x-74\right)}{x-74}=0\)
\(\Rightarrow\frac{x-74}{72}+\frac{x-74}{71}+\frac{x-74}{70}-\frac{x-74}{\frac{1}{3}\left(x-74\right)}=0\)
\(\Rightarrow\left(x-74\right)\left(\frac{1}{72}+\frac{1}{71}+\frac{1}{70}-\frac{1}{\frac{1}{3}\left(x-74\right)}\right)=0\)
\(\Rightarrow x-74=0\).Do \(\frac{1}{72}+\frac{1}{71}+\frac{1}{70}-\frac{1}{\frac{1}{3}\left(x-74\right)}\ne0\)
=>x=74
c)×+5/ 81 + ×+4/ 41 + ×-7/ 31 + 6 = 0
\(\Rightarrow\frac{x+5}{81}+1+\frac{x+4}{41}+2+\frac{x-7}{31}+3+\frac{6\left(x+86\right)}{x+86}=0\)
\(\Rightarrow\frac{x+86}{81}+\frac{x+86}{41}+\frac{x+86}{31}+\frac{x+86}{\frac{1}{6}\left(x+86\right)}=0\)
\(\Rightarrow\left(x+86\right)\left(\frac{1}{81}+\frac{1}{41}+\frac{1}{31}+\frac{1}{\frac{1}{6}\left(x+86\right)}\right)=0\)
\(\Rightarrow x+86=0\).Do \(\frac{1}{81}+\frac{1}{41}+\frac{1}{31}+\frac{1}{\frac{1}{6}\left(x+86\right)}\ne0\)
=>x=-86
d)tương tự nhé
Đặt \(A=3^{30}-3^{29}+3^{28}-...-3^1+3^0\)
\(3A=3^{31}-3^{30}+3^{29}-...-3^2+3^1\)
\(3A+A=\left(3^{31}-3^{30}+3^{29}-...-3^2+3^1\right)+\left(3^{30}-3^{29}+3^{28}-...-3^1+3^0\right)\)
\(4A=3^{31}-3^0\)
\(A=\frac{3^{31}-1}{4}\)
Chúc bạn học tốt ~
cảm ơn bạn T.T
Thank you very much! T.T