\(\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+\dfrac{1}{154}+\dfrac{1}{238}\)

\(=\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}+\dfrac{1}{14.17}\)

\(=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{14}-\dfrac{1}{17}\)

\(=\dfrac{1}{2}-\dfrac{1}{17}\)

\(=\dfrac{17}{34}-\dfrac{2}{34}\)

\(=\dfrac{15}{34}\)

\(1+4+7+10+...+94\)

Số số hạng dãy số là :

\(\left(94-1\right):3+1=32\) (số hạng)

Tổng dãy số là :

\(\left(94+1\right)\times32:2=1520\)

Đáp số :\(1520\)

\(\left(-\dfrac{1}{3}\right)^2.\dfrac{18}{-4}\)

\(=\dfrac{1}{9}.\dfrac{18}{-4}\)

\(=1.\dfrac{2}{-4}\)

\(=\dfrac{1}{-2}\)

\(\dfrac{2}{1.3}=\dfrac{2}{3}\)

\(1\dfrac{13}{15}.3.\left(0,5\right)^2.3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)

\(=\dfrac{28}{15}.3.0,25.3+\left(\dfrac{8}{15}-\dfrac{79}{60}\right):\dfrac{47}{24}\)

\(=\dfrac{28}{15}.3.\dfrac{1}{4}.3+\left(\dfrac{8}{15}-\dfrac{79}{60}\right):\dfrac{47}{24}\)

\(=\dfrac{28}{15}.3.\dfrac{1}{4}.3+\left(\dfrac{32}{60}-\dfrac{79}{60}\right):\dfrac{47}{24}\)

\(=\dfrac{28}{15}.3.\dfrac{1}{4}.3+-\dfrac{47}{60}:\dfrac{47}{24}\)

\(=\dfrac{28}{15}.3.\dfrac{1}{4}.3+-\dfrac{47}{60}.\dfrac{24}{47}\)

\(=\dfrac{28}{5}.\dfrac{3}{4}+-\dfrac{2}{5}\)

\(=\dfrac{7}{5}.3+-\dfrac{2}{5}\)

\(=\dfrac{21}{5}+-\dfrac{2}{5}\)

\(=\dfrac{19}{5}\)

5x = 125

x = 125 : 5

x = 25

Vậy x = 25

(x - 1/3).(1/2 - 3x) = 0

TH1:

x - 1/3 = 0

x = 1/3

TH2

1/2 - 3x = 0

3x = 0 - 1/2

3x = -1/2

x = -1/2 : 3

x = -1/6

Vậy x ϵ { - 1/6 ; 1/2}

Số số hạng dãy số là :

\(\left(2023-3\right):2+1=1011\) (số hạng)

Tổng là:

\(\left(2023+3\right)\times1011:2=1024143\)

Đáp số :...

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