Tính nhanh :
a) (34 . 53 + 33 . 54) : 33 . 53
b) 1282 . 97 : 366
c) 1515 : 314 : 513
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a ) 4 7 + 2 7 + 1 7 + 3 4 + 5 4 = 3 b ) − 5 7 + − 2 7 + − 1 5 + 3 4 + 1 4 = − 1 5
c ) 5 13 + 8 13 + − 5 7 + − 20 41 + − 21 41 = − 5 7 d ) 1 28 + 3 28 + 3 14 + − 1 14 + − 1 7 = 1 7 e ) 1 2 + − 1 2 + − 2 3 + 2 3 + 3 4 + − 3 4 + − 4 5 + 4 5 + 5 6 + − 5 6 = 0
80*33+97*33+34*97+33*17
=33*(80+97+17)+34*97
=33*194+34*97
=33*97*2+34*97
=97*(33*2+34)
=97*100
=9700
tik mik nha bn
a) \(3.5^2+15.2^2-26\div2\)
= 3.25 + 15.4 - 13
= 75 + 60 - 13
= 135 - 13
= 122
b) \(5^3.2-100\div4+2^3.5\)
= 125.2 - 25 + 8.5
= 250 - 25 + 40
= 225 + 40
= 265
c)\(6^2\div9+50.2-3^3.33\)
= 36 : 9 + 100 - 9.33
= 4 + 100 - 297
= 104 - 297
= -193
d)\(3^2.5+2^3.10-81\div3\)
= 9.5 + 8.10 - 27
= 45 + 80 - 27
= 125 - 27
= 98
e) \(5^{13}\div5^{10}-25.2^2\)
= 53 - 25.4
= 125 - 100
= 25
f) \(20\div2^2+5^9\div5^8\)
= 20 : 4 + 5
= 5 + 5
= 10
a) 5 13 + − 5 7 + − 20 41 + 8 13 + − 21 41 = 5 13 + 8 13 + − 20 41 + − 21 41 + − 5 7 = − 5 7
b) 1 28 + − 1 14 + 3 28 + − 1 7 + 3 14 = 1 28 + 3 28 + − 1 14 + 3 14 + − 1 7 = 1 7
c) 1 2 + − 2 3 + 3 4 + − 4 5 + 5 6 + − 5 6 + 4 5 + − 3 4 + 2 3 + − 1 2 = 1 2 + − 1 2 + 3 4 + − 3 4 + − 4 5 + 4 5 + 5 6 + − 5 6 = 0
\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)
\(b,3^2=9,3^3=27,3^4=81,3^5=243\)
\(c,4^2=16,4^3=64,4^4=256\)
\(d,5^2=25,5^3=125,5^4=625\)
\(B=3+3^2+3^3+3^4+...+3^{2009}+3^{2010}\)
\(=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{2009}+3^{2010}\right)\)
\(=3\left(1+3\right)+3^3\left(1+3\right)+...+3^{2009}\left(1+3\right)\)
\(=4.\left(3+3^3+...+3^{2009}\right)\)
⇒ \(B\) ⋮ 4
b: \(C=5\left(1+5+5^2\right)+...+5^{2008}\left(1+5+5^2\right)=31\cdot\left(5+...+5^{2008}\right)⋮31\)
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
a) (34 . 53 + 33 . 54) : 33 . 53
=[(33.53).(3+1+1+5)]
: 33 . 53
=[(33.53).10]:
33 . 53
=10
b) 1282 . 97 : 366
=(27)2.(32)7:(62)6
=214.314:612
=614:612
=62
c) 1515 : 314 : 513
=315.515:314:513
=315:314.515:513
=3.25
=75
a) \(\left(3^4.5^3+3^3.5^4\right):3^3.5^3\)
\(=3^3.5^3\left(3+5\right):3^3.5^3\)
\(=8\)(mình làm hơi tắt)
mình lm zậy thui nha mình bận lát nữa lm típ