1+2+2mu2+2mu3+...+2mu2006
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\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{20}}\)
=> \(2S=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{19}}\)
=> \(2S-S=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{19}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{20}}\right)\)
=> \(S=1-\frac{1}{2^{20}}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}\)
\(\Rightarrow\) \(\frac{1}{2}A=A-\frac{1}{2}=\frac{1}{2^{10}}-\frac{1}{2}\)
Vậy \(A=\left(\frac{1}{2^{10}}-\frac{1}{2}\right):\frac{1}{2}=\frac{2}{2^{10}}-1\)
Do đó \(A+\frac{1}{2^{10}}=\frac{2}{2^{10}}-1+\frac{2}{10}=1\)
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A= 4+2.2+2.2.2+2.2.2.2+.......+{2.2.2.2.2.....} có 20 thừa số 2
Có số số hạng ở trong khoảng số 2 là:
(20-2)+1=19(số)
Có 20 thừa số 2 suy ra:20.2=40
Tổng là:
(40+2)*19:2=399
A=4+399
A=403
**** nhé Hương Linh xinh xắn
A = 21 + 22 + ... + 22010
A.2 = 22 + 23 +... + 22011
A.2 - A = ( 22 + 23+ ... + 22011)- ( 2 + 22 + ... + 22010 )
A = 22011 - 2
**** cong chua xuka