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DT
2
YN
21 tháng 2 2022
`Answer:`
\dfrac15+\dfrac1{5+10}+\dfrac1{5+10+15}\ +\,.\!.\!.+\ \dfrac1{5+10+15\ +\,.\!.\!.+\ 100}\\=\dfrac15+\dfrac1{5.(1+2)}+\dfrac1{5.(1+2+3)}\ +\,.\!.\!.+\ \dfrac1{5.(1+2+3\ +\,.\!.\!.+\ 20)}\\=\dfrac15\left(1+\dfrac1{1+2}+\dfrac1{1+2+3}\ +\,.\!.\!.+\ \dfrac1{1+2+3\ +\,.\!.\!.+\ 20}\right)\\=\dfrac15\bigg(\dfrac22+\dfrac26+\dfrac2{12}\ +\,.\!.\!.+\ \dfrac2{20.21}\bigg)\\=\dfrac25\left(\dfrac1{1.2}+\dfrac1{2.3}+\dfrac1{3.4}\ +\,.\!.\!.+\ \dfrac1{20.21}\right)\\=\dfrac25\left(1-\dfrac12+\dfrac12-\dfrac13+\dfrac13-\dfrac14\ +\,.\!.\!.+\ \dfrac1{20}-\dfrac1{21}\right)\\=\dfrac25\left(1-\dfrac1{21}\right)\\=\dfrac25\!\cdot\!\dfrac{20}{21}\\=\dfrac8{21}
YN
21 tháng 2 2022
`Answer:`
Mình gửi lại bài nhé. Mong lần này không bị lỗi như lần trước.
\(\dfrac15+\dfrac1{5+10}+\dfrac1{5+10+15}\ +\,.\!.\!.+\ \dfrac1{5+10+15\ +\,.\!.\!.+\ 100}\\=\dfrac15+\dfrac1{5.(1+2)}+\dfrac1{5.(1+2+3)}\ +\,.\!.\!.+\ \dfrac1{5.(1+2+3\ +\,.\!.\!.+\ 20)}\\=\dfrac15\left(1+\dfrac1{1+2}+\dfrac1{1+2+3}\ +\,.\!.\!.+\ \dfrac1{1+2+3\ +\,.\!.\!.+\ 20}\right)\\=\dfrac15\bigg(\dfrac22+\dfrac26+\dfrac2{12}\ +\,.\!.\!.+\ \dfrac2{20.21}\bigg)\\=\dfrac25\left(\dfrac1{1.2}+\dfrac1{2.3}+\dfrac1{3.4}\ +\,.\!.\!.+\ \dfrac1{20.21}\right)\\=\dfrac25\left(1-\dfrac12+\dfrac12-\dfrac13+\dfrac13-\dfrac14\ +\,.\!.\!.+\ \dfrac1{20}-\dfrac1{21}\right)\\=\dfrac25\left(1-\dfrac1{21}\right)\\=\dfrac25\!\cdot\!\dfrac{20}{21}\\=\dfrac8{21}\)
11 tháng 10 2017
\(a,\dfrac{20^5.5^{10}}{100^5}=\dfrac{20^5.5^5.5^5}{100^5}=\dfrac{100^5.5^5}{100^5}=5^5\)
29 tháng 7 2018
\(\frac{20^5.5^{10}}{100^5}\)
\(=\frac{20^5.5^5.5^5}{100^5}\)
\(=\frac{100^5.5^5}{100^5}\)
\(=5^5\)
\(=3125\)
Học tốt !!! ~
29 tháng 7 2018
\(\frac{20^5\cdot5^{10}}{100^5}=\frac{4^5\cdot5^5\cdot5^{10}}{4^5\cdot25^5}=\frac{4^5\cdot5^5\cdot25^5}{4^5\cdot25^5}=5^5=3125\)
12 tháng 11 2021
c: \(=\dfrac{3}{2}\cdot1-1-20=\dfrac{3}{2}-21=\dfrac{-39}{2}\)
11 tháng 10 2015
\(\frac{20^5.5^{10}}{100^5}=\frac{20^5.25^5}{100^5}=\frac{\left(20.25\right)^5}{100^5}=\frac{500^5}{100^5}=5^5\)
LC
11 tháng 10 2015
\(\frac{20^5.5^{10}}{100^5}=\frac{20^5.\left(5^2\right)^5}{100^5}=\frac{20^5.25^5}{100^5}=\frac{\left(20.25\right)^5}{100^5}=\frac{500^5}{100^5}=\frac{\left(100.5\right)^5}{100^5}=\frac{100^5.5^5}{100^5}=5^5=3125\)
4 tháng 7 2016
\(\frac{20^5.5^{10}}{100^5}=\frac{4^5.5^5.25^5}{100^5}=\frac{100^5.5^5}{100^5}=5^5\)
\(\frac{20^5.5^{10}}{100^5}\)
\(=\frac{20^5.\left(5^2\right)^5}{100^5}\)
\(=\frac{20^5.25^5}{100^5}\)
\(=\frac{\left(20.25\right)^5}{100^5}\)
\(=\frac{500^5}{100^5}\)
\(=\left(\frac{500}{100}\right)^5\)
\(=5^5\)
_Chúc bạn học tốt_
\(\frac{20^5.5^{10}}{100^5}\)
\(=\frac{\left(2^2.5\right)^5.5^{10}}{2^2.5^2}\)
\(=\frac{2^{10}.5^5.5^{10}}{2^2.5^2}\)
\(=\frac{2^2.2^8.5^{15}}{2^2.5^2}\)
\(=\frac{2^8.5^2.5^{13}}{5^2}\)
\(=2^8.5^{13}\)