TÍNH BIỂU THỨC A=10^2-(5^2.4-4^3.3)+2^3
GIẢI CHI TIẾT NHÉ
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A = 102 - ( 52 . 4 - 43 . 3 ) + 23
A = 100 - ( 25 . 4 - 64 . 3 ) + 8
A = 100 - ( 100 - 192 ) + 8
A = 100 - ( - 92 ) + 8
A = 192 + 8
A = 200
10^2 - ( 5^2 . 4 - 4^3 . 3 ) + 2^3
= 100 - ( 25 . 4 - 64 . 3 ) + 8
= 100 - ( 100 - 192 ) + 8
= 100 - ( -92 ) + 8
= 192 + 8
= 200
= 251
\(x:\dfrac{1}{2}=\dfrac{3}{4}+\dfrac{5}{3}\\ \Rightarrow x:\dfrac{1}{2}=\dfrac{9}{12}+\dfrac{20}{12}\\ \Rightarrow x:\dfrac{1}{2}=\dfrac{29}{12}\\ \Rightarrow x=\dfrac{29}{12}\times\dfrac{1}{2}\\ \Rightarrow x=\dfrac{29}{24}\)
\(N=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2014.2016}\)
\(=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2014.2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2014}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1008}{2016}-\dfrac{1}{2016}\right)\)
\(=2.\dfrac{1007}{2016}=\dfrac{1007}{1008}\)
Công thức đây bạn:
\(\dfrac{a}{n\left(n+a\right)}=\dfrac{1}{n}-\dfrac{1}{n+a}\)
\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)
\(A=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+\frac{1}{\left(1+5\right).5:2}\)
\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{6}\right)\)
\(A=2.\frac{1}{3}=\frac{2}{3}\)
A=10^2-(5^2.4-4^3.3)+2^3
A=100-(25.4-64.3)+2^3
A=100-(100-192)+8
A=100-100+192+8
A=0+192+8
A=200