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Bài 1:
1. $2^n+2^{n+3}=144$
$2^n(1+2^3)=144$
$2^n.9=144$
$2^n=144:9=16=2^4\Rightarrow n=4$
2.
$3^n+3^{n+2}=270$
$3^n(1+3^2)=270$
$3^n.10=270$
$3^n=270:10=27=3^3\Rightarrow n=3$
3.
$2^n+2^{n+1}+2^{n+2}+2^{n+3}=960$
$2^n(1+2+2^2+2^3)=960$
$2^n.15=960$
$2^n=960:15=64=2^6$
$\Rightarrow n=6$
4.
$3^n+3^{n+1}+3^{n+2}+3^{n+3}=3240$
$3^n(1+3+3^2+3^3)=3240$
$3^n.40=3240$
$3^n=3240:40=81=3^4\Rightarrow n=4$
Bài 2:
1. $(x+1)^2=49=7^2$
$\Rightarrow x+1=7$
$\Rightarrow x=6$
2.
$(x+2)^3=512=8^3$
$\Rightarrow x+2=8\Rightarrow x=6$
3.
$(x-3)^9=(x-3)$
$\Rightarrow (x-3)^9-(x-3)=0$
$\Rightarrow (x-3)[(x-3)^8-1]=0$
$\Rightarrow x-3=0$ hoặc $(x-3)^8-1=0$
$\Rightarrow x-3=0$ hoặc $(x-3)^8=1=1^8=(-1)^8$
$\Rightarrow x=3$ hoặc $x-3=1$ hoặc $x-3=-1$
$\Rightarrow x=3$ hoặc $x=4$ hoặc $x=2$
A = 1/(5.6) + 1/(6.7) + ... + 1/(24.25)
= 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/24 - 1/25
= 1/5 - 1/25
= 4/25
B = 2/(1.3) + 2/(3.5) + 2/(5.7) + ... + 2/(99.101)
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 - 1/101
= 1 - 1/101
= 100/101
`a) A = 1/(5.6) + 1/(6.7)+...+1/(24.25)`
`= 1/5 - 1/6 + 1/6 - 1/7 +...+1/24-1/25`
`= 1/5-1/25`
`= 5/25 - 1/25`
`= 4/25`
Vậy:`A = 4/25`
`b) B = 2/(1.3)+2/(3.5)+...+2/(99.101)`
`= 1- 1/3 + 1/3 - .... +1/99-1/101`
`= 1 - 1/101`
`= 100/101`
Vậy: `B = 100/101`
\(A=\left(-1\right)+2-3+\left(-4\right)+5-6+\left(-7\right)+8-9\)
\(=2-1-3+5-4-6+8-7-9\)
\(=\left(2-1-3\right)+\left(5-4-6\right)+\left(8-7-9\right)\)
\(=\left(-2\right)+\left(-5\right)+\left(-8\right)\)
\(=-15\)
\(-\dfrac{13}{41}=\dfrac{-13.101}{41.101}=\dfrac{-1313}{4141}\) (1)
\(\dfrac{-13}{41}=\dfrac{-13.10101}{41.10101}=\dfrac{-131313}{414141}\)(2)
\(\dfrac{-13}{41}=\dfrac{-13.1010101}{41.1010101}=\dfrac{-13131313}{41414141}\)(3)
từ (1)(2)(3)=> \(\dfrac{-13}{41}=\dfrac{-1313}{4141}=\dfrac{-131313}{414141}=\dfrac{-13131313}{41414141}\)