A=3+3^2+3^3+...+3^2015+3^2016
tính A
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`(2bc-2016)/(3c-2bc+2016)`
`=(-(3c-2bc+2016)+3c)/(3c-2bc+2016)`
`=-1+(3c)/(3c-2bc+2016)`
`(2b)/(3-2b+ab)
`=(2bc)/(3c-2bc+abc)`
`=(2bc)/(3c-2bc+2016)`
`(4032-3ac)/(3ac-4032+2016a)`
`=(-(3ac-4032+2016a)+2016a)/(3ac-4032+2016a)`
`=-1+(2016a)/(3ac-2abc+2016a)`
`=-1+(2016)/(3c-2bc+2016)`
`=>M=-1+(3c)/(3c-2bc+2016)-(2bc)/(3c-2bc+2016)-1+(2016)/(3c-2bc+2016)
`=>M=-2+(3c-2bc+2016)/(3c-2bc+2016)`
`=>M=-2+1`
`=>M=-1`
`(2bc-2016)/(3c-2bc+2016)`
`=(-(3c-2bc+2016)+3c)/(3c-2bc+2016)`
`=-1+(3c)/(3c-2bc+2016)`
`(2b)/(3-2b+ab)`
`=(2bc)/(3c-2bc+abc)`
`=(2bc)/(3c-2bc+2016)`
`(4032-3ac)/(3ac-4032+2016a)`
`=(-(3ac-4032+2016a)+2016a)/(3ac-4032+2016a)`
`=-1+(2016a)/(3ac-2abc+2016a)`
`=-1+(2016)/(3c-2bc+2016)`
`=>M=-1+(3c)/(3c-2bc+2016)-(2bc)/(3c-2bc+2016)-1+(2016)/(3c-2bc+2016)`
`=>M=-2+(3c-2bc+2016)/(3c-2bc+2016)`
`=>M=-2+1`
`=>M=-1`
Nãy thiếu latex ạ sorry~~
\(\text{Ta có:}\)
\(\left(a-1\right)^3+\left(b-2\right)^3+\left(c-3\right)^3=\)
\(\left(a-1\right)^3+\left(b-2\right)^3+\left(c-3\right)^3-3\left(a-1\right)\left(b-2\right)\left(c-3\right)+3\left(a-1\right)\left(b-2\right)\left(c-3\right)=0\)
\(\Leftrightarrow\left(a+b+c-6\right)\left(....\right)+3\left(a-1\right)\left(b-2\right)\left(c-3\right)=0\)
\(\Leftrightarrow a=1\text{ hoặc }b=2\text{ hoặc }c=3\)
còn lại ko tính đc bạn ktra lại đề
Giải:
A=1+3+32+33+...+32015
3A=3+32+33+34+...+32016
3A-A=(3+32+33+34+...+32016)-(1+3+32+33+... +32015)
2A=32016-1
A=32016-1/2
⇒B-A
=32016:2-(32016-1):2
=(32016-32016+1):2
=1:2=1/2
Chúc bạn học tốt!
Xét bài toán :
So sánh \(\frac{a}{b}\)và \(\frac{a+m}{b+m}\)( a>b , m>0)
Có \(\frac{a}{b}=\frac{a\left(b+m\right)}{b\left(b+m\right)}=\frac{ab+am}{b\left(b+m\right)}\)
\(\frac{a+m}{b+m}=\frac{b\left(a+m\right)}{b\left(b+m\right)}=\frac{ab+bm}{b\left(b+m\right)}\)
Mà a>b => am > bm => \(\frac{ab+am}{b\left(b+m\right)}>\frac{ab+bm}{b\left(b+m\right)}\)hay \(\frac{a}{b}>\frac{a+m}{b+m}\)
Áp dụng : \(A=\frac{3^{2017}+5}{3^{2015}+5}>\frac{3^{2017}+5+4}{3^{2015}+5+4}=\frac{3^{2017}+9}{3^{2015}+9}=\frac{3^2\left(3^{2017}+9\right)}{3^2\left(3^{2015}+9\right)}\)
\(=\frac{3^{2015}+1}{3^{2013}+1}=B\)
=> A > B
NHân với 3