a) (-21) + | -50 | + (-29) – | -2016 |
b) 36 : 32 + 32 . 23 -150
c) ( 5103 – 5102 – 5101) : ( 599 . 26 – 599)
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a) (-21) + |-50| + (-29) – |-2016|
= (-21) + 50 + (-29) – 2016
= [(-21) + (-29) + 50] – 2016 = ( -50 +50 ) – 2016
= 0 – 2016 = - 2016 .
b) 36 : 3 2 + 3 2 . 2 3 - 15 0
= 36 : 9 + 9 . 8 – 1 = 4 + 72 – 1 = 76 – 1 = 75
c) ( 5 103 – 5 102 – 5 101 ) : ( 5 99 . 26 – 5 99 )
= ( 5 103 – 5 102 – 5 101 ) : 5 99 . ( 26 – 1 )
= ( 5 103 – 5 102 – 5 101 ) : ( 5 99 . 25 )
= 5 101 ( 5 2 – 5 1 – 5 0 ) : ( 5 99 . 5 2 )
= ( 5 101 . 19 ) : 5 101 = 19
c) ( 5 103 - 5 102 - 5 101 ) : ( 5 99 . 26 - 5 99 )
= ( 5 103 - 5 102 - 5 101 ) : [ 5 99 . ( 26 – 1)]
= ( 5 103 - 5 102 - 5 101 ) : ( 5 99 . 25 )
= 5 101 ( 52 – 51 – 50) : ( 5 99 . 52 )
= ( 5 101 . 19 ) : 5 101 = 19
Bài 1:
1) \(9A=3^3+3^5+...+3^{113}\)
\(\Rightarrow8A=9A-A=3^3+3^5+...+3^{113}-3-3^3-...-3^{111}=3^{113}-3\)
\(\Rightarrow A=\dfrac{3^{113}-3}{8}\)
2) \(9B=3^4+3^6+...+3^{202}\)
\(\Rightarrow8B=9B-B=3^4+3^6+...+3^{202}-3^2-3^4-...-3^{200}=3^{202}-3^2=3^{202}-9\)
\(\Rightarrow B=\dfrac{3^{202}-9}{8}\)
3) \(25C=5^3+5^5+...+5^{101}\)
\(\Rightarrow24C=25C-C=5^3+5^5+...+5^{101}-5-5^3-...-5^{99}=5^{101}-5\)
\(\Rightarrow C=\dfrac{5^{101}-5}{24}\)
4) \(25D=5^4+5^6+...+5^{102}\)
\(\Rightarrow24D=25D-D=5^4+5^6+...+5^{102}-5^2-5^4-...-5^{100}=5^{102}-25\)
\(\Rightarrow D=\dfrac{5^{102}-25}{24}\)
Bài 2:
a) Gọi d là UCLN(2n+1,n+1)
\(\Rightarrow\left\{{}\begin{matrix}2n+1⋮d\\n+1⋮d\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}2n+1⋮d\\2n+2⋮d\end{matrix}\right.\)
\(\Rightarrow\left(2n+2\right)-\left(2n+1\right)⋮d\Rightarrow1⋮d\)
Vậy 2n+1 và n+1 là 2 số nguyên tố cùng nhau
\(\Rightarrow\dfrac{2n+1}{n+1}\) là phân số tối giản
b) Gọi d là UCLN(2n+3,3n+4)
\(\Rightarrow\left\{{}\begin{matrix}2n+3⋮d\\3n+4⋮d\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}6n+9⋮d\\6n+8⋮d\end{matrix}\right.\)
\(\Rightarrow\left(6n+9\right)-\left(6n+8\right)⋮d\Rightarrow1⋮d\)
\(\Rightarrow\dfrac{2n+3}{3n+4}\) là phân số tối giản
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50=1275
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37
=(1+37)x37:2
=703
a) (-21) + | -50 | + (-29) – | -2016 |
= -21 + 50 - 29 -2016
= (-21 - 29 +50 ) -2016
= -2016
b) 36 : 32 + 32 . 23 -150 ( xem lại đề nhé )
c) ( 5103 – 5102 – 5101) : ( 599 . 26 – 599)
= ( 1 - 5101 ) : ( 599 . ( 26 - 1 ) )
= - 5100 : (599 . 25)
= \(-\frac{204}{599}\)