Tìm x biết:
2.22+3.23+4.24+...+x.2x=2x+10
Tìm số tự nhiên n biết 2.22 3.23 4.24 5.25 ........ n.2n = 2n 10
Thực hiện phép tính
a) 22024 - 22023 - 22022 - ... - 22 - 2 - 1
b) 1.2 + 2.22 + 3.23 + ... + 100.2100
c) \(\dfrac{6^{12}+15.2^{10}.3^{11}}{12.6^{11}}\)
2. Tìm x,y ∈ N biết
a) 13 + 2 (x+1) = 39
b) (2x . 3)3=125
c) 7 . 3x-1 + 11 . 3x+1=318
d) 13 - 2x chia hết cho x +1
e) 4x + 11 chia hết cho 3x +2
g) 2y+8 = 3x
Nhờ mn giải giúp e trước 6h sáng ngày mai với ạ, em cảm ơn
2:
a: =>2(x+1)=26
=>x+1=13
=>x=12
b: =>(6x)^3=125
=>6x=5
=>x=5/6(loại)
c: =>\(7\cdot3^x\cdot\dfrac{1}{3}+11\cdot3^x\cdot3=318\)
=>3^x=9
=>x=2
d: -2x+13 chia hết cho x+1
=>-2x-2+15 chia hết cho x+1
=>15 chia hết cho x+1
=>x+1 thuộc {1;3;5;15}
=>x thuộc {0;2;4;14}
e: 4x+11 chia hết cho 3x+2
=>12x+33 chia hết cho 3x+2
=>12x+8+25 chia hết cho 3x+2
=>25 chia hết cho 3x+2
=>3x+2 thuộc {1;-1;5;-5;25;-25}
mà x là số tự nhiên
nên x=1
1:
a: Đặt A=2^2024-2^2023-...-2^2-2-1
Đặt B=2^2023+2^2022+...+2^2+2+1
=>2B=2^2024+2^2023+...+2^3+2^2+2
=>B=2^2024-1
=>A=2^2024-2^2024+1=1
c: \(=\dfrac{3^{12}\cdot2^{11}+2^{10}\cdot3^{12}\cdot5}{2^2\cdot3\cdot3^{11}\cdot2^{11}}=\dfrac{2^{10}\cdot3^{12}\left(2+5\right)}{2^{13}\cdot3^{12}}\)
\(=\dfrac{7}{2^3}=\dfrac{7}{8}\)
tính a/b biết a=1/1.21 + 1/2.22 + 1/3.23 + ... +1/80.100; b=1/1.81 + 1/2.82 + 1/3.82 + ... + 1/20.100
20a = 20/1.21 + 20/2.22+ ... + 20/80.100
= 1-1/21 + 1/2 - 1/22 +...+ 1/80 - 1/100
= 1 + 1/2 + 1/3 +... + 1/19 + 1/20 - 1/81 - 1/82 -.... - 1/100
80b = 80/1.81 + 80/2.82 + 80/3.83 +... + 80/20.100
= 1 - 1/81+ 1/2 - 1/83 +...+ 1/20 - 1/100
=> 20a = 80b
=> a/b = 4
S = 2+2.22+3.23 +... +2016.22016
1) Chứng tỏ S+2013 chia hết cho 22017+1
2) Tìm số dư khi chia S cho 8
\(S=2+2.2^2+3.2^3+...+2016.2^{2016}\)
\(2S=2^2+2.2^3+3.2^4+...+2016.2^{2017}\)
\(2S-S=S=\text{}\text{}\text{}\text{}2^2+2.2^3+3.2^4+...+2016.2^{2017}-2-2.2^2-3.2^3-...-2016.2^{2016}\)
\(S=2\left(0-1\right)+2^2\left(1-2\right)+2^3\left(2-3\right)+...+2^{2016}\left(2015-2016\right)+2^{2017}.2016\)
\(S=-\left(2+2^2+2^3+...+2^{2016}\right)+2^{2017}.2016\)
\(\)Đặt \(A=2+2^2+2^3+...+2^{2016}\)
\(2A=2^2+2^3+2^4+...+2^{2017}\)
\(2A-A=A=2^2+2^3+2^4+...+2^{2017}-2-2^2-2^3-...-2^{2016}\)
\(A=2^{2017}-2\)
Thay vào S ta được:
\(S=-2^{2017}+2+2^{2017}.2016\)
\(S=2^{2017}.2015+2\)
Ta có \(S+2013=2^{2017}.2015+2+2013\)
\(S+2013=2^{2017}.2015+2015\)
\(S+2013=2015\left(2^{2017}+1\right)\)
Suy ra \(S+2013⋮2^{2017}+1\)
Vậy \(S+2013⋮2^{2017}+1\) (đpcm)
\(S=2+2.2^2+3.2^3+...+2016.2^{2016}\)
\(S=2+2^3+3.2^3+...+2016.2^{2016}\)
\(S=2+2^3\left(1+3+...+2016.2^{2013}\right)\)
\(S=2+8.\left(1+3+...+2016.2^{2013}\right)\)
Suy ra \(S\) chia \(8\) dư \(2\)
Vậy \(S\) chia \(8\) dư \(2\)
Gửi bạn nha, bài này làm hơi dài ^^
Câu 24 : Cho A = 1/1.21 + 1/2.22 + 1/3.23 + ...+ 1/80.10
tìm x:
a) 2x - 15= 52 .3
b) 3x+1 -12 = 3.23
c) (x+1)+(x+20 + ....+ (x+100)= 5750
a) 2x - 15= 52.3
2x - 15= 25.3
2x - 15 = 75
2x = 75 + 15
2x = 90
x = 90 : 2
x = 45
b) 3x+1 - 12 = 3.23
3x+1 - 12 = 69
3x+1 = 69 + 12
3x+1 = 81
=> 3x+1 = 34
=> x + 1 = 4
=> x = 4 - 1
=> x = 3
c) mk ko hiểu đề lắm =\
a) 58 + 7x = 100
b) 4(x- 51) = 2.22 + 20
c) 2x – 49 = 5.32
a)58+7x=100
⇔7x=42
⇔x=6
b)4(x-51)=2.22+20
⇔4x-204=28
⇔4x=232
⇔x=58
c)2x-49=5.32
⇔2x-49=45
⇔2x=94
⇔x=47
Câu 24 : Cho A = 1.21 + 1/2.22 + 1/3.23 + ... + 1/80.100 ; B = 1/1.81 + 1/2.82 + 1/3.83 + ... + 1/20.100 . Tính A/B
Cho \(A=\dfrac{1}{1.21}+\dfrac{1}{2.22}+\dfrac{1}{3.23}+...+\dfrac{1}{80.100}\);
\(B=\dfrac{1}{1.81}+\dfrac{1}{2.82}+\dfrac{1}{3.83}+...+\dfrac{1}{20.100}\).
Tính \(\dfrac{A}{B}\).
A=20/1.21+20/2.22+...+20/80.100
=1-1/21+1/2-1/22+...+1/80-1/100
=(1+1/2+...+1/80)-(1/21+1/22+...+1/100)
80B=80/1.81+80/2.82+...+8/20.100
=1-1/81+1/2-1/82+...+1/20-1/100
=(1+1/2+...+1/20)-(1/81+1/82+...+1/100)
=(1+1/2+1/3+...+1/20+1/21+1/22+...+1/80)-(1/21+1/22+...1/80+1/81+1/82+...1/100)
=>20A=80B
=>A=4B
tìm x biết:
-2x(x+3)+x(2x-1)=10
-2x(x + 3) + x(2x - 1) = 10
-2x² - 6x + 2x² - x = 10
-7x = 10
x = -10/7