Đặt A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\)

     2A = \(2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\right)\)

      2A = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)

 2A - A = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\right)\)

         A = \(1+\frac{1}{2^{100}}=\frac{2^{100}+1}{2^{100}}\)

\(-\frac{7}{11}.\frac{11}{19}+\frac{-7}{11}.\frac{8}{19}+\frac{-4}{11}=-\frac{7}{11}.\left(\frac{11}{19}+\frac{8}{19}\right)-\frac{4}{11}\)

\(=-\frac{7}{11}.1-\frac{4}{11}=-\frac{7}{11}-\frac{4}{11}\)

\(=-\frac{11}{11}=-1\)

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)

\(B=\frac{1.2.3...19}{2.3.4...20}\)

\(B=\frac{1}{20}\)

B=(1-1/2)(1-1/3)........(1-1/20)

B=1/2.2/3.......19/20

B=1/20

5x+9: x+1

\(\Leftrightarrow\)5*(x+1)+4:x+1

\(\Rightarrow\)5*(x+1)\(⋮\)x+1

\(\Rightarrow\)4 \(⋮\)x+1

\(\Rightarrow\)x+1\(\in\)Ư(4) =\(\hept{\begin{cases}\\\end{cases}}\)1;2;4;-1;-2;-4

\(\Rightarrow\)x\(\hept{\begin{cases}\\\end{cases}}\)0;1;3;-2;-3;-5

Vậy x\(\in\)-----------------------

(5x + 9) : (x + 1)

<=> (5x + 5) + 4 : x+1

<=> 5(x+1) + 4 : x+1

<=>  4 : x+1

<=> x+1 thuộc Ư(4)

<=> x+1 thuộc { 1;-1;2;-2;4;-4}

<=> x+1 thuộc { 0;-2;-3;3;-5 }

dấu chia là dấu chia hết nha

\(B=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)....\left(1+\frac{1}{99}\right)\)

     \(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}\)

      \(=\frac{3.4.5....100}{2.3.4...99}\)

Chúc bạn học tốt !

        \(=50\)

số số hạng: (100-1):1+1=100

tổng trên là: (100+1).100:2=5050

k nhoa

Tổng của dãy số đó là:

\(1+2+...+100=\left(100+1\right)\cdot\frac{100}{2}=5050\)

Đáp số:\(5050\)

5/6x+5/4=2

5/6x=3/4

x=9/10

\(\left(\frac{5}{6}x+\frac{5}{4}\right)\div\frac{3}{2}=\frac{4}{3}\)

\(\frac{5}{6}x+\frac{5}{4}=\frac{4}{3}\cdot\frac{3}{2}\)

\(\frac{5}{6}x+\frac{5}{4}=2\)

\(\frac{5}{6}x=2-\frac{5}{4}\)

\(\frac{5}{6}x=\frac{8}{4}-\frac{5}{4}\)

\(\frac{5}{6}x=\frac{3}{4}\)

\(x=\frac{3}{4}\div\frac{5}{6}\)

\(x=\frac{3}{4}\cdot\frac{5}{6}\)

\(x=\frac{1}{4}\cdot\frac{5}{2}\)

\(x=\frac{5}{8}\)

=1/2(2/1.3+2/3.5+2/5.7+....+2/2009.2011

=1/2(1/1-1/3+1/3-1/5+1/5-1/7+....+1/2009-1/2011

=1/2(1/1-1/2011)

=1/2.2010/2011

=1005/2011

=1/1-1/3+1/3-1/5+1/5-1/7+....+1/2009-2011

=1-1/2011

=2010/1011