b=1/4+1/16+1/64+1/256+...+1/16384
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a: 4A=4+4^2+...+4^9
=>3A=4^9-1
=>A=(4^9-1)/3
b: 2A=1+1/2+...+1/2^7
=>A=1-1/256=255/256
c: =1-1/5+1/5-1/9+...+1/85-1/89
=1-1/89=88/89
d: =1/3(3/1*4+3/4*7+...+3/304*307)
=1/3(1-1/4+1/4-1/7+...+1/304-1/307)
=1/3*306/307=102/307
e: E=1-1/2+1/2-1/3+...+1/11-1/12
=1-1/12=11/12
g: =2/5(1-1/6+1/6-1/11+...+1/96-1/101)
=2/5*100/101=40/101
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\(16+64+256+1024+...+16384+65536\)
\(=4^2+4^3+4^4+....+4^7+4^8\)
Đặt : \(A=4^2+4^3+4^4+....+4^7+4^8\)
\(\Rightarrow4A=4^3+4^4+4^5+...+4^8+4^9\)
\(\Rightarrow4A-A=\left(4^3+4^4+4^5+...+4^8+4^9\right)-\left(4^2+4^3+4^4+...+4^7+4^8\right)\)
\(\Rightarrow3A=4^9-4^2\)
\(\Rightarrow A=\frac{4^9-4^2}{3}=87376\)
Vậy : \(16+64+256+1024+...+16384+65536=87376\)
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\(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+...+\frac{1}{16384}\)
\(A=\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{14}}\)
\(2^2A=1+\frac{1}{2^2}+...+\frac{1}{2^{12}}\)
\(4A-A=\left(1+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)-\left(\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{14}}\right)\)
\(3A=1-\frac{1}{2^{14}}\)
\(A=\frac{1-\frac{1}{2^{14}}}{3}\)
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A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{64}\) + \(\dfrac{1}{128}\) + \(\dfrac{1}{256}\)
2A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{64}\) + \(\dfrac{1}{128}\)
2A - A = 1 - \(\dfrac{1}{256}\)
A = \(\dfrac{255}{256}\)
???
b= 1/4 +1/16+1/64+1/256+...+1/16384
4b = 1+ 1/4 +1/16 + 1/64+... +1/4096
4b-b = 1 -1/16384
3b = 16383/16384
b = 49149/16384