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a) x+2x+...+50x =2550
x. [ 1+2+3+....+50]=2550
ta co :
so so hang cua day 1;2;3;4;...;50:
[50-1]:1+1=50
tong cua day tren la :
[50+1].50:2=1275
=> x.1275=2550
x=2550:1275
vay x=2
3.(x+1)^3 = -81
=> (x+1)^3 = -81 : 3 = -27
=> (x+1)^3 = (-3)^3
=> x+1 = -3
=> x = -3 - 1
=> x = -4
Vậy x = -4
Tk mk nha
Đặt \(A=1+2+2^2+2^3+...+2^{20}\)
\(2A=2+2^2+2^3+2^4+...+2^{21}\)
\(2A-A=\left(2+2^2+2^3+...+2^{21}\right)-\left(1+2+2^2+...+2^{20}\right)\)
\(A=2^{21}-1\)
Ta đặt
A= 1+2^1+2^2+2^3+....2^20
2A= 21+22+23+....+221
=>2A-A=(2^1+2^2+2^3+...+2^21)-(1+2^2+2^3+...)
1A=2^21-1
Vậy A=2^21-1
\(S=5+5^1+5^2+5^3+...+5^{2024}\)
\(=5+\left(5^1+5^2+5^3+5^4\right)+\left(5^5+5^6+5^7+5^8\right)+...+\left(5^{2021}+5^{2022}+5^{2023}+5^{2024}\right)\)
\(=5+\left(5^1+5^2+5^3+5^4\right)+5^4\left(5^1+5^2+5^3+5^4\right)+...+5^{2020}\left(5^1+5^2+5^3+5^4\right)\)
\(=5+780\left(1+5^4+...+5^{2020}\right)\)
Có \(780⋮65\)nên \(780\left(1+5^4+...+5^{2020}\right)⋮65\)
suy ra \(S\)chia cho \(65\)dư \(5\).
B1:
Ta có: \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}-2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}-2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1-5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}\)
\(=\frac{2.\left(-4\right)}{3.5}=-\frac{8}{15}\)
B2:
Ta có: \(1+3+5+...+x=1600\)
\(\Leftrightarrow\frac{\left(x+1\right)\cdot\left(\frac{x-1}{2}+1\right)}{2}=1600\)
\(\Leftrightarrow\left(x+1\right)\cdot\frac{x+1}{2}=3200\)
\(\Leftrightarrow\left(x+1\right)^2=6400\)
Xét theo dãy tăng tiến ta thấy được giá trị của x càng tăng
=> x dương => x + 1 dương
\(\Rightarrow x+1=80\)
\(\Rightarrow x=79\)
1)-(-3)3-(2x+1)3=152
27-(2x+1)3=152
(2x+1)3=27-152
(2x+1)3=-125
(2x+1)3=(-5)3
2x+1=-5
2x=-4
x=-4:2
x=-2
Vậy x=-2