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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
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a. \(A=2+2^2+2^3+2^4+2^5+...+2^{200}\)
\(2A=2^2+2^3+2^4+2^5+2^6+...+2^{201}\)
\(2A-A=2^{201}-2\)
b. \(Tacó:2^1=2;2^2=4;2^3=8;2^4=..6;2^5=2;2^6=4;...\)
Cứ dựa theo quy luật trên, ta có:
\(2^{4k+1}=..2;2^{4k+2}=...4;2^{4k+3}=...8;2^{4k}=..6\)
\(=>2^{201}=2^{4.50+1}\)
\(=>2^{101}=...2\)
\(=>2^{201}-2=..2-2\)\(=0\)
Vậy A có tân cùng là 0
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\(\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}\)
\(\Rightarrow\) \(\frac{1}{2}A=A-\frac{1}{2}=\frac{1}{2^{10}}-\frac{1}{2}\)
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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\(B=1+2+2^2+...+2^6.\)
\(=>4B=2^2+2^3+...+2^8\)\(\left(1\right)\)
\(A=2^2+2^3+...+2^8\)\(\left(2\right)\)
Từ (1) và (2)
=> A = 4B