.........................

= \(\frac{1}{2}\). ( \(\frac{2}{1.3}\) + \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) ... +  \(\frac{2}{x.\left(x+2\right)}\) )

= \(\frac{1}{2}\) . ( 1 - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{5}\) +  \(\frac{1}{5}\) - \(\frac{1}{7}\) + ... + \(\frac{1}{x}\)-  \(\frac{1}{x+2}\) ) 

= ................ 

Bạn tự làm tiếp nhé ! Chúc bạn học tốt :)

 Các bạn ơi! giải chi tiết ra cho mình luôn nha 

\(2^{16}=2^{13+3}=2^{13}.2^3=8.2^{13}\)

Vì 8 > 7 nên \(8.2^{13}>7.2^{13}\)

\(\Rightarrow2^{16}>7.2^{13}\)

2^16=2^3.2^13=8.2^13   mà 8>7 =>  7.2^13<8.2^13    => 7.2^13<2^16

\(\frac{1}{2}.\left(\frac{4}{3}+\frac{2}{5}\right)-\frac{3}{4}.\left(\frac{8}{9}+\frac{16}{3}\right)\)

\(=\frac{1}{2}.\left(\frac{20}{15}+\frac{6}{15}\right)-\frac{3}{4}.\left(\frac{8}{9}+\frac{48}{9}\right)\)

\(=\frac{1}{2}.\frac{26}{15}-\frac{3}{4}.\frac{56}{9}\)

\(=\frac{13}{15}-\frac{14}{3}\)

\(=-\frac{19}{5}\)

\(\frac{1}{2}.\left(\frac{4}{3}+\frac{2}{5}\right)-\frac{3}{4}.\left(\frac{8}{9}+\frac{16}{3}\right)\)

\(=\left(\frac{1}{2}.\frac{4}{3}+\frac{1}{2}.\frac{2}{5}\right)-\left(\frac{3}{4}.\frac{8}{9}+\frac{3}{4}.\frac{16}{3}\right)\)

\(=\left(\frac{2}{3}+\frac{1}{5}\right)-\left(\frac{2}{3}+4\right)\)

\(=\frac{2}{3}+\frac{1}{5}-\frac{2}{3}-4\)

\(=\frac{1}{5}-4\)

\(=\frac{1}{5}-\frac{20}{5}=\frac{-19}{5}\)

\(A=\frac{2^2}{1.3}\cdot\frac{3^2}{2.4}....\frac{999^2}{998.1000}\)

\(A=\frac{2^2.3^2....999^2}{1.3.2.4.998.100}=\frac{\left(2.3.....999\right)\left(2.3....999\right)}{\left(1.2....998\right)\left(3.4....1000\right)}\)

\(A=999\cdot\frac{1}{500}=\frac{999}{500}\)( khúc này mk làm tắt, bn bỏ dấu ở trên rồi bỏ từng tử)

=?????????????????????????????????????????????????????????????????????????????????????????????????????????????????

\(B=\frac{2^2}{1.3}+\frac{2^2}{3.5}+...+\frac{2^2}{195.197}=2\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{195.197}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{195}-\frac{1}{197}\right)=2\left(1-\frac{1}{197}\right)=2.\frac{196}{197}=\frac{392}{197}\)

5A=\(\frac{1}{5}+\frac{2}{5^2}...+\frac{n}{5^n}...+\frac{11}{5^{11}}\)

=>4A=5A-A=\(\frac{1}{5}+\frac{1}{5^2}...+\frac{1}{5^{11}}-\frac{11}{5^{12}}\)

=>20A=\(1+\frac{1}{5}+...+\frac{1}{5^{10}}-\frac{11}{5^{11}}\)

=>16A=20A-4A=\(1-\frac{1}{5^{11}}+\frac{11}{5^{12}}-\frac{11}{5^{11}}\)

Mà \(1-\frac{1}{5^{11}}< 1\),\(\frac{11}{5^{12}}-\frac{11}{5^{11}}< 0\)

=>16A<1

Do đó: A<1/16(đpcm)

cho địt t trả lời

1/4+2/5+6/8+2/15+6/7

=(1/4+6/8)+(2/5+2/15)+6/7

=(2/8+6/8)+(6/15+2/15)+6/7

=1+8/15+6/7

=1+56/105+90/105

=1+146/105

=1+105/105+41/105

=1+1+41/105

=2+41/105

=2 và 41/105

2 và 41/105 là hỗn số nha

1/4+2/5+6/8+2/15+6/7

Ta có:

1/4=1-3/4

6/8=3/4

2/15=2/3*5=1/3-1/5

==> 1-3/4+2/5+3/4+1/3-1/5+6/7 

=1+1/3+1/5+6/7

=(105+35+21+90)/105

=251/105.

Th1:x^2+/2x-2/=x+x^2-1

/2x-2/=x+x^2-1-x^2

/2x-2/=x-1+x^2-x^2

/2x-2/=x-1

+)nếu x-1=2x-2 thì

x-2x=-2+1

-x=-1

x=1

+) nếu x-1=-(2x-2) thì

x+2x=2+1

3x=3

x=1

Vậy th1 x=1

Th2:-(x^2+/2x-2/)=x+x^2-1

Tương tự

Kb mk giúp