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\(S=4+4^1+4^2+...+4^{30}\)
\(4S=4^2+4^2+4^3+...+4^{31}\)
\(4S-S=\left(4^2+4^2+4^3+...+4^{31}\right)-\left(4+4+4^2+...+4^{30}\right)\)
\(3S=4^2+4^{31}-4-4\)
\(3S=4^{31}+8\)
\(S=\frac{4^{31}+8}{3}\)
S=4+42+43+......+430
4S=4(4+42+43+.....+430)
4S=42+43+.....+430+431
Lấy 4s -s ,ta có:
: 4S=42+43+....+431
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S=4+42+...+430
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3S=431-4
Suy ra S=(431-4):3
Vậy S= (431-4) : 3
Thi tốt nhé
a/ \(A=1+3+3^2+..........+3^{55}\)
\(\Leftrightarrow3A=3+3^2+...........+3^{55}+3^{56}\)
\(\Leftrightarrow3A-A=\left(3+3^2+........+3^{56}\right)-\left(1+3+....+3^{55}\right)\)
\(\Leftrightarrow2A=3^{56}-1\)
\(\Leftrightarrow A=\frac{3^{56}-1}{2}\)
\(4S=4^1+4^2+...+4^{36}\)
\(\Leftrightarrow3S=4^{36}-1\)
hay \(S=\dfrac{4^{36}-1}{3}\)
\(\Leftrightarrow3\cdot S=4^{36}-1< 4^{36}=64^{12}\)
Dễ thấy:\(64^{12}=\left(4^3\right)^{12}=4^{3.12}=4^{36}\)
Ta có: 4S=\(4\left(4^0+4^1+4^2+4^3+...+4^{35}\right)\)
\(=4^1+4^2+4^3+4^4+...+4^{36}\)
=>4S-S=\(4^{36}-4^0\)
Hay 3S=\(4^{36}-1< 4^{36}=64^{12}\)
Vậy 3S<\(64^{12}\)
Ta có : S=4\(^0\)+4\(^1\)+4\(^2\)+4\(^3\)+ ... + 4\(^{35}\)
Ta thấy : 64\(^{12}\)=(4\(^3\))\(^{12}\)=4\(^{3.12}\)=4\(^{36}\)
Ta sẽ có : 4S=4.(4\(^0\)+4\(^1\)+4\(^2\)+4\(^3\)+ ... + 4\(^{35}\))
=4\(^1\)+4\(^2\)+4\(^3\)+ 4\(^4\)... + 4\(^{36}\)
\(\Rightarrow\)4S-S=4\(^{36}\)-4\(^0\)
Hay : 3S=4\(^{36}\)-1<4\(^{36}\)=64\(^{12}\)
Vậy : 3S<64\(^{12}\)
Ta có: \(S=4^0+4^1+...+4^{35}\)
\(\Rightarrow4S=4+4^1+...+4^{36}\)
\(\Rightarrow4S-S=\left(4+4^1+...+4^{36}\right)-\left(4^0+4^1+...+4^{35}\right)\)
\(\Rightarrow3S=4^{36}-4^0\)
\(\Rightarrow3S=\left(4^3\right)^{12}-1\)
\(\Rightarrow3S=64^{12}-1\)
Vì \(64^{12}-1< 64^{12}\) nên \(3S< 64^{12}\)
Vậy \(3S< 64^{12}\)
Ta có: S=40+41+...+435S=40+41+...+435
⇒4S=4+41+...+436⇒4S=4+41+...+436
⇒4S−S=(4+41+...+436)−(40+41+...+435)⇒4S−S=(4+41+...+436)−(40+41+...+435)
⇒3S=436−40⇒3S=436−40
⇒3S=(43)12−1⇒3S=(43)12−1
⇒3S=6412−1⇒3S=6412−1
Vì 6412−1<64126412−1<6412 nên 3S<64123S<6412
Vậy 3S<6412
Ta có:
3s1=3+32+33+34+...+350
=>3s1-s1=3+32+33+34+...+350-1-3-32-33-...-349
=>2s1=350-1
=>a1=(350-1)/2
Tính s2 tương tự như s1
ta lấy 4s2-s2 đoực kết quả s2=(450-1)/3
S1 = 1+3+32+33+34+..........+349
3S1 = 3+32+33+34+35+.........+350
3S1 - S1 = 3+32+33+34+35+.........+350 - (1+3+32+33+34+..........+349)
= 3+32+33+34+35+.........+350 - 1 - 3 - 32 - 33 - 34-..........-349
2S1 = 350 - 1
S1 =\(\frac{3^{50}-1}{2}\)
\(S=4+4^1+4^2+4^3+.........+4^{29}+4^{30}\)
\(\Rightarrow4S=4^2+4^2+4^3+4^4+........+4^{31}\)
\(\Rightarrow4S-S=3S=4^{31}+4.2\)
rất chuẩn