Lời giải:
$A=(1+2-3-4-5)+(6+7-8-9-10)+(11+12-13-14-15)+....+(2011+2012-2013-2014-2015)+(2016+2017-2018-2019-2020)$

$=(-9)+(-14)+(-19)+....+(-2019)+(-2024)$

$=-(9+14+19+...+2019+2024)$

Số số hạng: $(2024-9):5+1=404$
$A=-(2024+9).404:2=-410666$

\(\dfrac{12}{17}.\dfrac{5}{7}-\left(-\dfrac{12}{17}\right).\dfrac{1}{7}+\dfrac{1}{17+7}\)

\(=\dfrac{12}{17}.\dfrac{5}{7}+\dfrac{12}{17}.\dfrac{1}{7}+\dfrac{1}{24}\)

\(=\dfrac{12}{17}\left(\dfrac{5}{7}+\dfrac{1}{7}\right)+\dfrac{1}{24}\)

\(=\dfrac{12}{17}.\dfrac{6}{7}+\dfrac{1}{24}\)

\(=\dfrac{72}{119}+\dfrac{1}{24}=\dfrac{1847}{2856}\)

Ta có:

\(B=\frac{10}{7.12}+\frac{10}{12.17}+...+\frac{10}{2017.2022}\)

\(\Rightarrow B=2.\left(\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{2017.2022}\right)\)

\(\Rightarrow B=2.\left(\frac{12-7}{7.12}+\frac{17-12}{12.17}+...+\frac{2022-2017}{2017.2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{2022}\right)\)

\(\Rightarrow B=\frac{2015}{7077}\)

* là sao vậy???

có nghĩa là nhân

=> S*15 = 7*12*(17-2) + 12*17*(22-7) + 17*22*(27-12) +...+2017*2022*(2027-2012)

= 7*12*17-2*7*12+12*17*22-7*12*17+...+2017*2022*2027-2012*2017*2022

=2017*2022*2027-2*7*12=8266864098 - 168= 8266863930

\(\frac{15}{32}\)

\(\frac{15}{32}\)

a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)

= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)

= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)

= 1 - 1 - \(\dfrac{11}{25}\)

= - \(\dfrac{11}{25}\)

b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)

= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))

= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)

= - \(\dfrac{499}{35}\)

c, \(\dfrac{1}{8}\) + \(\dfrac{1}{24}\) + \(\dfrac{1}{48}\)+ ...+ \(\dfrac{1}{2400}\)

= \(\dfrac{1}{2\times4}\)  +\(\dfrac{1}{4\times6}\) + \(\dfrac{1}{6\times8}\) +...+ \(\dfrac{1}{48\times50}\)

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{2\times4}\) +\(\dfrac{2}{4\times6}\)+ \(\dfrac{2}{6\times8}\) +...+ \(\dfrac{2}{48\times50}\))

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\) +...+ \(\dfrac{1}{48}\) - \(\dfrac{1}{50}\))

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{50}\))

= \(\dfrac{1}{2}\) \(\times\) \(\dfrac{12}{25}\)

= \(\dfrac{6}{25}\)

2/5 + 3/4 = 23/40

7/12 - 2/7 + 1/12 =  25/84 + 1/12 = 8/21

12/17 - 5/17 - 4/17 =  3/17

OK

\(\frac{2}{5}+\frac{3}{4}=\frac{8}{20}+\frac{15}{20}=\frac{23}{20}\)

\(\frac{7}{12}-\frac{2}{7}+\frac{1}{12}=\left(\frac{7}{12}+\frac{1}{12}\right)-\frac{2}{7}=\frac{2}{3}-\frac{2}{7}=\frac{14}{21}-\frac{6}{21}=\frac{8}{21}\)

\(\frac{12}{17}-\frac{5}{17}-\frac{4}{17}=\frac{12-5-4}{17}=\frac{3}{17}\)

trần thanh hải sai con đầu bằng 23/20 mới đúng