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a) \(D=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)
\(\Rightarrow7D=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\)
\(\Rightarrow7D-D=\left(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\right)-\left(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\right)\)
\(\Rightarrow6D=1-\frac{1}{7^{100}}\)
\(\Rightarrow D=\left(1-\frac{1}{7^{100}}\right).\frac{1}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
-.-? lớp 6
Có \(\left(5x-7\right)\left(2x+3\right)-\left(7x+2\right)\left(x-4\right)\)
\(=10x^2+15x-14x-21-7x^2+28x-2x+8\)
\(=\left(10x^2-7x^2\right)+\left(15x-14x+28x-2x\right)+\left(-21+8\right)\)
\(=3x^2+27x-13\)
Thay x = 1/2 vào biểu thức đã rút gọn
\(\Rightarrow3\left(\frac{1}{2}\right)^2+27.\frac{1}{2}-13=\frac{5}{4}\)
Vậy giá trị biểu thức là 5/4
(5x-7)(2x+3)-(7x+2)(x-4)
=10x2+15x-14x-21-(7x2-7x+2x-8)
=10x2-x-21-7x2+7x-2x+8
=3x2+4x-13
Thay x=1/2 vào BT ta được:
3*(1/2)2+4*1/2-13
=3/4+2-13
=3/4-11
=-41/4
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\(7^{n+4}-7^n=7^n.7^4-7^n=7^n.\left(7^4-1\right)=7^n.2400\) chia hết cho 30
\(=125+\left(81+4\right).2+\left(27-3\right):4\)
\(=125+85.2+\left(27-3\right):4\)
\(=125+85.2+24:4\)
\(=125+170+24:4\)
\(=125+170+6\)
\(=295+6\)
\(=301\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1+(2-3-4+5)+(6-7-8+9)+.....+(2006-2007-2008+2009)+2010
= 1+0+0+.....+0+2010 = 2011
k mk nha
xin lỗi sai
(206+1).106:2=21321