5 | - | 3 | = | |
7 | 9 |
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\(a,79-\left(79-2021\right)=79-79+2021=2021\\ b,4^5:4^3-8=4^2-8=16-8=8\\ c,17.\left(-85\right)+17.85=\left(-17\right).85+17.85=85\left(17-17\right)=85.0=0\)
a) 79 - (79 - 2021) = 79 - 79 + 2021 = 2021
b) 45 : 43 - 8 = 42 - 8 = 16 - 8 = 8
c) 17 . (- 85) + 17 . 85 = 17 . (- 85 + 85) = 17 . 0 =0
a: =-79+47+52-20
=99-99
=0
b: \(=67-19-48-15=-15\)
c: \(=\left(-8\right)\cdot14+17\cdot3=-112+51=-61\)
d: \(=37+48-72-30=7-24=-17\)
Với mọi \(n\in\text{ℕ*}\), ta có:
\(\dfrac{2}{n\sqrt{n+2}+\left(n+2\right)\sqrt{n}}\)\(=\dfrac{2\left(n\sqrt{n+2}-\left(n+2\right)\sqrt{n}\right)}{\left(n+2\right)^2n-n^2\left(n+2\right)}\)\(=\dfrac{2\left[\left(n+2\right)\sqrt{n}-n\sqrt{n+2}\right]}{n\left(n+2\right)}\)\(=\dfrac{1}{\sqrt{n}}-\dfrac{1}{\sqrt{n+2}}\)
Vậy ta có:
\(2A=\dfrac{1}{\sqrt{1}}-\dfrac{1}{\sqrt{3}}+\dfrac{1}{\sqrt{3}}-\dfrac{1}{\sqrt{5}}+...-\dfrac{1}{\sqrt{81}}\)
\(=1-\dfrac{1}{\sqrt{81}}\)
\(A=\dfrac{1-\dfrac{1}{\sqrt{81}}}{2}\)
a)\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{-3}{5}.\dfrac{2}{7}+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-2}{5}+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}.\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{-3}{5}\)
=\(\dfrac{-2}{5}.1+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}+\dfrac{-3}{5}\)
=\(-\dfrac{5}{5}\) = -1
\(\dfrac{5}{9}.\dfrac{14}{17}+\dfrac{1}{17}.\dfrac{5}{9}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{5}{9}.\left(\dfrac{14}{17}+\dfrac{1}{17}\right)+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{5}{9}.\dfrac{15}{17}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{25}{51}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{691}{612}\)
\(236.146+236.855-236\)
\(=236.\left(146+855-1\right)\)
\(=236.1000\)
\(=236000\)
\(16.75+25.16-1300+2020^0\)
\(=16.\left(75+25\right)-1300+1\)
\(=1600-1300+1\)
\(=301\)
#)Giải :
\(\left(\frac{3}{79}\right)^{20}\cdot\left(\frac{3}{-79}\right)^{19}=\left(\frac{3}{79}\right)^{20}\cdot\left(\frac{3}{79}\right)^{19}=\left(\frac{3}{79}\right)^{39}\)
\(\left(\frac{2}{3}\right)^5:\left(\frac{2}{-3}\right)^3=\left(\frac{2}{3}\right)^5:\left(\frac{2}{3}\right)^3=\left(\frac{2}{3}\right)^2\)
a)=\(\frac{-2.4}{5.7}+\frac{-3.2}{5.7}+\frac{-3}{5}\)
=\(\frac{-2.4}{5.7}+\frac{-2.3}{5.7}+\frac{-3}{5}\)
=\(\frac{-2}{5}\left(\frac{4+3}{7}\right)+\frac{-3}{5}\)
=\(\frac{-2}{5}.1+\frac{-3}{5}\)
=-1
b)
\(\left(-3-5\right)^2.\left(-79+82\right):\left(-2\right)\)
\(=\left(-8\right)^2.3:\left(-2\right)\)
\(=64.3:\left(-2\right)\)
\(=-96\)
\(\left(-3-5\right)^2.\left(-79+82\right):\left(-2\right)\)
\(=\left(-8\right)^2.3:\left(-2\right)\)
\(=64.3.\frac{-1}{2}\)
\(=192.\frac{-1}{2}\)
\(=-96\)
= 8/21