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Lời giải:
Xét tử số:
$X=1+2+2^2+2^3+...+2^{2008}$
$2X=2+2^2+2^3+2^4+....+2^{2009}$
$\Rightarrow 2X-X=(2+2^2+2^3+2^4+....+2^{2009})-(1+2+2^2+...+2^{2008})$
$\Rightarrow X=2^{2009}-1$
$\Rightarrow S=\frac{X}{1-2^{2009}}=\frac{2^{2009}-1}{-(2^{2009}-1)}=-1$
Cho S= 1/3 +2/3^2+3/3^3+..+100/3^100 So sánh 5^2019 và 5^2020
Hiện tại mình đang cần gấp giúp mk nha!
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\(5^{2019}< 5^{2020}\)
vì
2020>2019
=>\(5^{2019}< 5^{2020}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=1+2+2^2+...+2^{99}\)
\(S=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{98}+2^{99}\right)\)
\(S=3+2^2.3+...+2^{98}.3\)
\(=3\left(1+2^2+...+2^{98}\right)⋮3\)
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A = 20 + 21 + 22 + 23 +....+ 22002
2A = 21 + 22 + 23 + 24 +....+ 22003
2A - A = ( 21 + 22 + 23 + 24 +....+ 22003 ) - ( 20 + 21 + 22 + 23 + .... + 22002 )
A = 22003 - 1
Hk tốt
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1.S1=1 - 2 + 3 - 4 + ... + 1997 - 1998 + 1999
= (1 - 2) + ...+(1997 - 1998) + 1999
= -1 + -1 + ...+-1 + 1999
SH:1998 : 2
= 999 . -1
= -999
TDS:-999 + 1999
= 1000
b.S2=1 - 4 + 7 - 10 + ...- 2998+3001
= (1 - 4) + (7 - 10) + ...+ (2995 - 2998) + 3001
= -3 + -3 + ...+-3 + 3001
= (2998 - 1) : 3 + 1
= 1000 . -3
= -3000 + 3001
= 1
câu b mình làm lộn :
S2=1000 : 2
= 500 . -3
=-1500 + 3001
= 1501
KẾT QUẢ RA 1501 NHA
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=3+3^2+3^3+...........+3^{100}\)
\(\Leftrightarrow\)\(3S=3^2+3^3+3^4+...........+3^{101}\)
\(\Leftrightarrow\)\(3S-S=3^{101}-3\)
\(\Leftrightarrow\)\(2S=3^{101}-3\)
\(\Leftrightarrow\)\(S=\frac{3^{101}-3}{2}\)
Vậy \(S=\frac{3^{101}-3}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2\left|x-1\right|+3\left(x+2\right)=3^2\)
\(2\left|x-1\right|+3x+6=9\)
\(2\left|x-1\right|=9-3x-6\)
\(2\left|x-1\right|=3-3x\)
\(\left|x-1\right|=\frac{3-3x}{2}\)
\(\Rightarrow\orbr{\begin{cases}x-1=\frac{3-3x}{2}\\x-1=-\frac{3-3x}{2}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3-3x}{2}+\frac{2}{2}\\x=\frac{-3+3x}{2}+\frac{2}{2}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3-3x+2}{2}\\x=\frac{-3+3x+2}{2}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5-3x}{2}\\x=\frac{-1+3x}{2}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=5-3x\\2x=-1+3x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}5x=5\\x=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=1\end{cases}}\)
S=1+2+2^2+2^3+...+2^2002
2S=2+2^2+2^3+2^4+...+2^2003
2S-S=(2+2^2+2^3+2^4+...+2^2003)-(1+2+2^2+2^3+...+2^2002)
2S-S=(2-2)+(2^2-2^2)+(2^3-2^3)+...+(2^2002-2^2002)+(2^2003-1)
S=0+0+0+...+0+(2^2003-1)
S=2^2003-1 (rút gọn)
tick nha
S=1+2+2^2+2^3+...+2^2002
=>2S=2+22+23+24+...+22013
=>2S-S=2+22+23+24+...+22013-1-2-22-23-...-22012
=>S=22013-1