a) 4 x 52 - 64 : 24
= 4 x 25 - 64 : 16
= 100 - 4 = 96
c) 1 - 2+ 3 - 4 + 5 - ...+ 2017
= (1 - 2) + (3 - 4) + (5 - 6) +...+ (2015 - 2016 ) + 2017
= (-1) + (-1) + (-1) + ...+ (-1) + 2017
= (-1) x 1008 + 2017
= (- 1008) + 2017
= 1009
b) 9 x 8 x 14 + 6 x ( -17) x ( - 12) + 19 x ( -4) x 18
= 1008 + 1224 - 1368
= 864
\(a,4.5^2-64:2^4\)
\(=100-4=96\)
\(b,1-2+3-4+5-...+2017\)
\(=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(2015-2016\right)+2017\)
Mỗi nhóm có kết quả là -1 và số nhóm sẽ là:
\(\left[\left(2016-1\right)+1\right]:2=1008\)
\(\Rightarrow=1008.\left(-1\right)+2017\)
\(=-1008+2017=1009\)
c, Gọi \(A=1-3+3^2-3^3+3^4-...-3^{2017}\)
\(\Rightarrow3A=3-3^2+3^3-3^4+..+3^{2018}\)
\(\Rightarrow3A+A=\left(3-3^2+3^3-3^4+...+3^{2018}\right)+\left(1-3+3^2-3^3+3^4-...-3^{2017}\right)\)
\(\Rightarrow4A=1+\left(3-3\right)+\left[\left(-3^2\right)+3^2\right]+...+\left(3^{2017}-3^{2017}\right)+3^{2018}\)
\(4A=1+3^{2018}\Rightarrow A=\dfrac{1+3^{2018}}{4}\)
a)\(4.5^2-64:2^4=100-4=96\)
b)\(9.8.14+6.\left(-17\right).\left(-12\right)+19.\left(-4\right).18\)
\(=18.4.14+18.17.4+\left(-19\right).4.18\)
=\(18.\left[4.\left(14+17-19\right)\right]\)
=\(18.\left[4.12\right]=18.48=864\)
c)1-2+3-4+5-...+2017
\(=1-2+\left(3-4\right)+\left(5-6\right)+...+\left(2015-2016\right)+2017\)
Từ 2016 đến 3 có số cặp là:\(\left[\left(2016-3\right):1+1\right]:2=1007\) cặp.Mà mỗi cặp có giá trị là:-1
Vậy:1-2+3-4+5-...+2017=1-2+(-1).1007+2017=1009
d)Đặt A=\(1-3+3^2-3^3+3^4-...-3^{2017}\)
\(\Rightarrow3A=3-3^2+3^3-3^4+3^5-...-3^{2018}\)
\(\Rightarrow3A+A=3-3^2+3^3-3^4+3^5-...-3^{2018}+1-3+3^2-3^3+3^4-3^5-...-3^{2017}\)\(\Rightarrow4A=-3^{2018}+1\)
\(\Rightarrow A=\dfrac{-3^{2018}+1}{4}\)
Bài 1 Tính hợp lí
a)\(4\times5^2-64\div2^4=100-4=96\\\)
d) A= \(1-3+3^2-3^3+3^4-...-3^{2017}\) (1)
=> 3A =\(3-3^2+3^3-3^4+3^5-...-3^{2018}\) (2)
Cộng (1) với (2) ta có:
4A = 1 \(-\) 32018
=> A = \(\dfrac{1-3^{2018}}{4}\)
