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a) \(9\cdot8\cdot14+6\cdot\left(-17\right)\cdot\left(-12\right)+19\cdot\left(-4\right)\cdot18\)
\(=1008+1224-1368\\ =864\)
b) \(1-2+3-4+5-...+2015\)
\(=\left(1-2\right)+\left(3-4\right)+...+\left(2013-2014\right)+2015\) (1007 ngoặc đơn)
\(=-1-1-1-..-1+2015\)
\(=-1\cdot1007+2015\\ =-1007+2015\\ =1008\)
a) \(4.5^2-32:2^5\)
\(=4.25-2^5:2^5\)
\(=100-1\)
\(=99.\)
b) \(9.8.14+6.\left(-17\right)\left(-12\right)+19.\left(-4\right).18\)
\(=9.2.4.14+6.3.\left(-4\right)\left(-17\right)+76.18\)
\(=18.56+18.68+18.76\)
\(=18\left(56+68+76\right)\)
\(=18\left(132+68\right)\)
\(=18.200\)
\(=3600.\)
c) \(\left(\dfrac{-1}{2}\right)^3-2.\left(\dfrac{-1}{2}\right)^2+3.\left(\dfrac{-1}{2}\right)+1\)
\(=\left(\dfrac{-1}{2}\right)\left[\left(\dfrac{-1}{2}\right)^2+2.\dfrac{-1}{2}+3\right]+1\)
\(=\left(\dfrac{-1}{2}\right)\left[\dfrac{1}{4}+\left(-1\right)+3\right]+1\)
\(\)\(=\left(\dfrac{-1}{2}\right)\left[\dfrac{1}{4}+2\right]+1\)
\(=\left(\dfrac{-1}{2}\right).\dfrac{9}{4}+1\)
\(=\dfrac{-9}{8}+1\)
\(=\dfrac{-1}{8}\)
a) =9x8x14+6x17x12+19x18x(-4)
=3x3x2x2x2x2x7+2x2x2x3x3x17-19x3x3x2x2x2
=2x2x2x3x3x(2x7+17-19)
=72x12
=864
số số hạng là :
( 1000000 - 1 ) : 1 + 1 = 1000000
tổng là :
( 1000000 + 1 ) x 1000000 : 2 = 500000500000
đáp số : 500000500000
Bài 1.
Đặt (12n + 1; 30n + 2) = d
\(\Rightarrow\) \(\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}5\left(12n+1\right)⋮d\\2\left(30n+2\right)⋮d\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}60n+5⋮d\\60+4⋮d\end{matrix}\right.\)
\(\Rightarrow\) (60n + 5) - (60n + 4) \(⋮\) d
\(\Rightarrow\) 1 \(⋮\) d
\(\Rightarrow\) d = 1
\(\Rightarrow\) (12n + 1; 30n + 2) = 1
Vậy phân số \(\dfrac{12n+1}{30n+2}\) là phân số tối giản
\(8.9.14+6.17.12+19.4.18\)
\(=4.2.9.14+6.3.17.4+19.4.18\)
\(=4.18.14+18.4.17+19.4.18\)
\(=4.18.\left(14+17+19\right)\)
\(=4.18.50\)
\(=3600\)