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a: \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3^6}{9}-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(81-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
=0
b: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)
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Đặt A = 1 + 3 + 32 + 33 + .... + 32000
3A = 3(1 + 3 + 32 + 33 + .... + 32000)
= 3 + 32 + 33 + 34 + .... + 32001
3A - A = (3 + 32 + 33 + 34 + .... + 32001 ) - (1 + 3 + 32 + 33 + .... + 32000)
2A = 32001 - 1
\(\Rightarrow A=\frac{3^{2001}-1}{2}\)
ĐẶT A LÀM BIỂU THỨC 1+3+3^2+3^3+..+3^2000
=>3A=3+3^2+3^3+.....+3^2001
=>3A-A=(1+3+3^2+3^3+..+3^2000)-(3+3^2+3^3+......+3^2001)
=>A=3^2001-1/3
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th1: \(\left(\frac{y}{3}-5\right)^{2008}-\left(\frac{y}{3}-5\right)^{2000}=0\)
\(\left(\frac{y}{3}-5\right)^{2000}.\left[\left(\frac{y}{3}-5\right)^8-1\right]=0\)
\(=>\orbr{\begin{cases}\left(\frac{y}{3}-5\right)^{2000}=0\\\left(\frac{y}{3}-5\right)^{2008}-1=0\end{cases}}\)
\(=>\orbr{\begin{cases}\frac{y}{3}=5=>y=15\\\frac{y}{3}=6=>y=18,\frac{y}{3}=4=>y=12\end{cases}}\)
Vậy ...
P/S: cái đoạn\(\left(\frac{y}{3}-5\right)^{2008}-1=0\)vì số mũ chẵn nên y=18 hay bằng 12 nha!
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Đặt BT trên là A ta có
\(3A=3+3^2+3^3+3^4+...+3^{2000}+3^{2001}\)
\(2A=3A-A=3^{2001}-1\)
\(A=\frac{3^{2001}-1}{2}\)
A= 1+3+32+33+...+32000
3A= 3+32+33+34+.. .+32001
3A-A=(3+32+33+34+.. .+32001)-(1+3+32+33+...+32000)
2A= 32001-1
A =(32001-1) :2
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Đề : Cho A= 1+3+32+33+34+...+32000. Biết 2A=3n-1
Tìm n
Đặt A=1/3+1/3^2+1/3^3+...+1/3^2000
=>3A=1+1/3+1/3^2+ ...+1/3^1999
=>3A-A=(1+1/3+1/3^2+...+1/3^1999)-(1/3+1/3^2+1/3^3+...+1/3^2000)
=>2A=1-1/3^2000
=>A=(1-1/3^2000)/2