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\(B=3^2+3^3+...+3^{99}\)
\(3B=3^3+3^4+...+3^{100}\)
\(3B-B=\left(3^3+3^4+...+3^{100}\right)-\left(3^2+3^3+...+3^{99}\right)\)
\(2B=3^{100}-3^2\)
\(B=\frac{3^{100}-9}{2}\)
\(2B+9=3^{2n+4}\)
\(\Leftrightarrow3^{2n+4}=3^{100}\)
\(\Leftrightarrow2n+4=100\)
\(\Leftrightarrow n=48\).
â) Ta có : \(2n-1⋮n+1\Leftrightarrow2n+2-2-1⋮n+1\)
\(\Leftrightarrow2\left(n+1\right)-2-1⋮n+1\)\(\Leftrightarrow2\left(n+1\right)-3⋮n+1\)
\(\Leftrightarrow2n-1⋮n+1\)khi \(3⋮n+1\Rightarrow n+1\in\)Ước của \(3\) \
\(\Leftrightarrow n+1\in\left(1;-1;3;-3\right)\)
\(\Leftrightarrow n\in\left(0;-2;2;-4\right)\)
Vậy \(n\in\left(-4;-2;0;2\right)\)
b) Ta có :\(9n+5⋮3n-2\Rightarrow3\left(3n-2\right)+6+5⋮3n-2\)
\(\Rightarrow3\left(3n-2\right)+11⋮3n-2\)
\(\Rightarrow9n+5⋮3n-2\)Khi \(11⋮3n-2\)
\(\Rightarrow3n-2\in U\left(11\right)\)
\(\Rightarrow3n-2\in\left(-11;-1;1;11\right)\)
\(\Rightarrow n\in\left(-3;1;\right)\)
Phần c) bạn tự làm nhé!
15 + ( x : 5 - 1 ) = 24
15 + ( x : 5 - 1 ) = 16
x : 5 - 1 = 16 - 15
x : 5 - 1 = 1
x : 5 = 1 + 1
x : 5 = 2
x = 10
Vậy x = 10
a) \(...=16.\left(36-37\right)=16.\left(-1\right)=-16\)
b) \(...=9.3+9.50=9.\left(3+50\right)=9.53=477\)
c) \(...=2.\left(\left(5.16-18\right)+36:18\right)=2.\left(70+2\right)=2.72=144\)
d) \(...=5\left(48:8+44\right)=5\left(6+44\right)=5.50=250\)
e) \(...=20-6=14\)
f) \(...=50+13-2=61\)
a) 16 . 36 - 16 . 37
= 16 . (36 - 37)
= 16 . (-1)
= -16
b) 36 : 4 . 3 + 9 . 50
= 9 . 3 + 9 . 50
= 9 . (3 + 50)
= 9 . 53
= 477
c) 2 . (5 . 16 - 18) + 36 : 18 . 2
= 2 . (80 - 18) + 2 . 2
= 2 . 62 + 2 . 2
= 2 . (62 + 2)
= 2 . 64
= 128