1 + 5/2 +5/8 +5/16 + 5/32 + 5/64
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tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
9 tháng 5 2023
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
DS
24 tháng 3 2016
Đặt \(A=1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(=5\cdot\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
Đặt \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(\Rightarrow2\cdot B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow B=2\cdot B-B=1-\frac{1}{64}=\frac{63}{64}\)
\(\Rightarrow A=5\cdot\frac{63}{64}=\frac{315}{64}\)
G
1
DD
Đoàn Đức Hà
Giáo viên
22 tháng 6 2021
\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{64}-1\right)\)
DQ
0
AK
2
29 tháng 6 2016
\(A=\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
...
\(4A=5^{64}-1\)
\(\Rightarrow A=\frac{5^{64}-1}{4}>B=\frac{5^{64}-1}{5}\)
BP
1
T
6
26 tháng 6 2017
5/2 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64
= 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32
=> 2A - A = 1 - 1/64
=> A = 1 - 1/64
Do đó : 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) = 5(1 - 1/64) = 5 . 63/64 = 315/64