\(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}\)\(+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)

\(=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

\(=\frac{1}{4}+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

\(=\frac{1}{4}+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

\(=\frac{1}{4}+\left(\frac{1}{2}-\frac{1}{6}\right)\)

\(=\frac{1}{4}+\frac{1}{3}\)

\(=\frac{7}{12}\)

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`a, 1/2 +1/3 +1/4`

`= 6/12 + 4/12 + 3/12`

`= (6+4+3)/12`

`= 13/12`

`b,5/2 -1/3 +1/4`

`= 30/12 - 4/12 + 3/12`

`=(30-4+3)/12`

`= 29/12`

`c, 1/2 . 1/3 +1/2 . 2/3`

`= 1/2. (1/3+2/3)`

`= 1/2. 3/3`

`=1/2 .1`

`=1/2`

`d, 3/2 - 1/3 +2/5`

`= 45/30 - 10/30 + 12/30`

`=(45-10+12)/30`

`= 47/30`

1/² là 1² hả bạn?

Hay sao?

\(A=\frac{61}{168}\)

999/1000

1/1.2+1/2.3+1/3.4+1/4.5+.................+1/9990999.9991000

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.................+1/9990999-1/9991000

=1-1/9991000

=9990999/9991000

\(A=-\dfrac{1}{2.3}-\dfrac{1}{3.4}-\dfrac{1}{4.5}-...-\dfrac{1}{9.10}\)

\(\Rightarrow-A=\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+\dfrac{5-4}{4.5}+...+\dfrac{10-9}{9.10}=\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)

\(=\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{2}{5}\Rightarrow A=-\dfrac{2}{5}\)

chế vừa thôi cụ

a: \(B=\left(4\cdot2^5\right):\left(2^3\cdot\frac{1}{16}\right)\)

\(=\left(4\cdot32\right):\left(\frac{8}{16}\right)\)

\(=128:\frac12=128\cdot2=256\)

b: \(B=3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^3}\)

\(=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=\frac{3^8}{3^8}\cdot3^2=3^2=9\)

c: \(D=\left\lbrace\left(0,1\right)^2\right\rbrace^0+\left\lbrack\left(\frac17\right)^1\right\rbrack^2:\frac{1}{49}\cdot\left\lbrack\left(2^2\right)^3:2^5\right\rbrack\)

\(=1+\left(\frac17\right)^2\cdot49\cdot2^6:2^5\)

\(=1+49\cdot\frac{1}{49}\cdot2=1+2=3\)

d: \(C=\left(-0,5\right)^5:\left(-0,5\right)^3-\left(\frac{17}{2}\right)^7:\left(\frac{17}{2}\right)^6\)

\(=\left(-0,5\right)^{5-3}-\left(\frac{17}{2}\right)\)

\(=\left(-0,5\right)^2-\frac{17}{2}=0,25-\frac{17}{2}=\frac14-\frac{34}{4}=-\frac{33}{4}\)