7/1.5+7/5.10+7/10.15+....+7/205.210
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\(=\dfrac{\left[7^{10}\cdot12+7^{10}\cdot15\right]}{7^8\cdot\left(-3\right)^3}=\dfrac{7^{10}\cdot27}{7^8\cdot\left(-27\right)}=-7^2=-49\)
\(\dfrac{1}{5.10}+\dfrac{1}{10.15}+...+\dfrac{1}{395.400}\\ =\dfrac{1}{5}\left(\dfrac{5}{5.10}+\dfrac{5}{10.15}+...+\dfrac{5}{395.400}\right)\\ =\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{395}-\dfrac{1}{400}\right)\\ =\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{400}\right)\\ =\dfrac{1}{5}.\dfrac{79}{400}\\ =\dfrac{79}{2000}\)
\(\dfrac{2}{5.10}+\dfrac{2}{10.15}+...+\dfrac{2}{995.1000}\\ =2\left(\dfrac{1}{5.10}+\dfrac{1}{10.15}+...+\dfrac{1}{995.1000}\right)\\ =\dfrac{2}{5}\left(\dfrac{5}{5.10}+\dfrac{5}{10.15}+...+\dfrac{5}{995.1000}\right)\\ =\dfrac{2}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{995}-\dfrac{1}{1000}\right)\\ =\dfrac{2}{5}\left(\dfrac{1}{5}-\dfrac{1}{1000}\right)\)
\(=\dfrac{2}{5}.\dfrac{199}{1000}\\ =\dfrac{199}{2500}\)
5/5.10 + 5/10.15 + ... + 5/45.50
= 1/5 - 1/10 + 1/10 - 1/15 + ... + 1/45 - 1/50
= 1/5 - 1/50
= 9/50
\(\frac{13}{10}\times\frac{15}{7}-\frac{8}{7}\times\frac{4}{3}+2=\frac{39}{14}-\frac{32}{21}+2=\frac{137}{42}\)
+ Ta có:
+ Vì hai điện tích trái dấu nên lực tương tác là lực hút => Chọn B
ko biet lam tu lam nhe
\(\frac{7}{1.5}+\frac{7}{5.10}+\frac{7}{10.15}+...+\frac{7}{205.210}=\frac{7}{5}\left(\frac{5}{1.5}+\frac{5}{5.10}+\frac{5}{10.15}+...+\frac{5}{205.210}\right)\)
\(=\frac{7}{5}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{205}-\frac{1}{210}\right)\)
\(=\frac{7}{5}.\left(1-\frac{1}{210}\right)\)
\(=\frac{7}{5}.\frac{209}{210}\)
\(=\frac{209}{150}\)
Study well ! >_<