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S = 1 + 31 + 32 + 33 + ... + 330
3S = 3 + 32 + 33 + 34 + ... + 331
3S - S = (3 + 32 + 33 + 34 + ... + 331) - (1 + 31 + 32 + 33 + ... + 330)
2S = 331 - 1
\(S=\frac{3^{31}-1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
K CHO MK NHA
Giải
S=1+1/3+1/6+1/10+...+1/45
=> S=2/2+2/6+2/12+2/20+.......+2/90
=>S=2/1x2 + 2/2x3 +2/3x4+......+2/9x10
=>S=2x(1/1x2 + 1/2x3 +....+1/9x10)
=>S=2x(1/1 - 1/2 + 1/2 - 1/3 +......+ 1/9 - 1/10
=>S=2x(1/1 - 1/10)
Vì 1/1-1/10<1=>2x(1/1 - 1/10)>2x1=2
Hay S<2
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S=3-32+33-34+....-32012
<=> 3S=32-33+34-35+....-32013
<=> 3S+S=(32-33+34-35+....-32013)+(3-32+33-34+....-32012)
<=> 4S=-32013+3
<=> \(S=\frac{-3^{2013}+3}{4}\)
\(S=3-3^2+3^3-3^4+........+-3^{2012}\)
\(\Rightarrow3S=3^2-3^3+3^4-3^5+..........-3^{2013}\)
\(\Rightarrow3S+S=4S=3^{2013}+3\)\(\Rightarrow S=\frac{3^{2013}+3}{4}\)
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S = 1 - 2 + 22 - 23+.....+ 22012 - 22013
2\(\times\)S = 2 - 22 + 23-.......- 22012 + 22013 - 22014
2 \(\times\) S + S = 1 - 22014
3S = 1 - 22014
3S - 22014 = 1 - 22014 - 22014 = 1 - 2.22014 = 1- 22015
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=3+3^2+3^3+........3^2012
=> 3S=3^2+3^3+........3^2013
=> 3S-S=2S=(3^2+3^3+........3^2013)-(3+3^2+3^3+........3^2012)
=> 2S=3^2013-3
=> S= \(\frac{3^{2013}-3}{2}\)