n 3^o7 I #_Jan_#
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a)
Cl | Cl0 |
HCl | Cl-1 |
HClO | Cl+1 |
KMnO4 | Mn+7 |
K2MnO4 | Mn+6 |
MnCl2 | Mn+2 |
Mn | Mn0 |
b)
FeO | Fe+2 |
FeCl3 | Fe+3 |
Fe3O4 | Fe+8/3 |
Fe2O3 | Fe+3 |
K2Cr2O7 | Cr+6 |
CrCl3 | Cr+3 |
Cr2(SO4)3 | Cr+3,S+6 |
HNO3 | N+5 |
H2SO4 | S+6 |
H2S | S-2 |
Na2SO4 | S+6 |
\(M_{R_2Cr_2O_7}=252\)
=>2R+52*2+7*16=252
=>2R=36
=>R=18
=>R là Ag
Công thức là \(Ag_2Cr_2O_7\)
\(1.M_{MgCl_2}=24+35,5\cdot2=95g/mol\\ 2.M_{BaCO_3}=137+12+16\cdot3=197g/mol\\ 3.M_{Cr_2O_7}=52\cdot2+16\cdot7=216g/mol\\ 4.M_{KMnO_4}=39+55+16\cdot4=158g/mol\\ 5.M_{Fe_2\left(SO_4\right)_3}=56\cdot2+\left(32+16\cdot4\right)\cdot3=400g/mol\\ 6M_{Al\left(OH\right)_3}=27+\left(16+1\right)\cdot3=78g/mol\\ 7.M_{NaBr}=23+80=103g/mol\\ 8.M_{ZnS}=65+32=97g/mol\\ 9.M_{Hg\left(NO_3\right)_2}=201+\left(14+16\cdot3\right)\cdot2=325g/mol\\ 10.M_{PbCO_3}=207+12+16\cdot3=267g/mol\)
Chứng minh rằng :
\(a.\)
\(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
\(b.\)
\(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
\(.a.\) \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
Ta có : \(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n.\left(3^2+2\right)-2^n.\left(2^2+1\right)\)
\(=3^n.10-2^{n-1}.2.5\)
\(=3^n.10-2^{n-1}.10\)
\(=10.\left(3^n-2^{n-1}\right)⋮10\) \(\left(dpcm\right)\)
Vậy : \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
\(.b.\) \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
Ta có : \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\) \(=3^n.\left(3^3+3\right)+2^n.\left(2^3+2^2\right)\)\(=3^n.30+2^n.12\)
\(=6\left(3^n.5+2^{n+1}\right)⋮6\) \(\left(dpcm\right)\)
Vậy : \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
a)\(VT=3^{n+2}-2^{n+2}+3^n-2^n\)
\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)
\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot2\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10\)
\(=10\cdot\left(3^n-2^{n-1}\right)⋮10\)
b)\(VT=3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=\left(3^{n+3}+3^{n+1}\right)+\left(2^{n+3}+2^{n+2}\right)\)
\(=3^{n+1}\left(3^2+1\right)+2^{n+2}\left(2+1\right)\)
\(=3^{n+1}\cdot10+2^{n+2}\cdot3\)
\(=3^n\cdot3\cdot2\cdot5+2^{n+1}\cdot2\cdot3\)
\(=3^n\cdot5\cdot6+2^{n+1}\cdot6\)
\(=6\cdot\left(3^n\cdot5+2^{n+1}\right)⋮6\)
Ta có: \(M=3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=3^{n+1}\left(3^2+1\right)+2^{n+2}\left(2+1\right)\)
\(=3^n\cdot3\cdot10+2^n\cdot4\cdot3\)
\(=6\left(5\cdot3^n+2^n\cdot2\right)⋮6\)(đpcm)
a/ \(I=lim\dfrac{5^n+2^n}{3^n+4^n}=lim\dfrac{1+\left(\dfrac{2}{5}\right)^n}{\left(\dfrac{3}{5}\right)^n+\left(\dfrac{4}{5}\right)^n}=\dfrac{1}{0}=+\infty\)
b/ \(I=lim\dfrac{\sqrt{n^3+2n}+3n}{n+\sqrt{n^2+1}}=lim\dfrac{\sqrt{\dfrac{n^3}{n^3}+\dfrac{2n}{n^3}}+\dfrac{3n}{n^{\dfrac{3}{2}}}}{\dfrac{n}{n^{\dfrac{3}{2}}}+\sqrt{\dfrac{n^2}{n^3}+\dfrac{1}{n^3}}}=\dfrac{1}{0}=+\infty\)
c/ \(I=lim\left[n\left(\sqrt{2+\dfrac{n}{n^2}}-\sqrt{1+\dfrac{2n}{n^2}+\dfrac{3}{n^2}}\right)\right]=+\infty.\left(\sqrt{2}-1\right)=+\infty\)
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