Thu gọn biểu thức:
A=1+1/2+1/2^2+1/2^3+...+1/2^2014
Những câu hỏi liên quan
21 tháng 11 2021 lúc 13:33
Rút gọn biểu thức:
A = \(\dfrac{1}{2+\sqrt{3}}\) + \(\dfrac{1}{2-\sqrt{3}}\)
Rút gọn biểu thức:A=1+1/2+1/22+1/23+...+1/22012
Ta có :
\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)
\(2A=1+2+\frac{1}{2}+...+\frac{1}{2^{2011}}\)
\(2A-A=\left(1+2+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)
\(A=2-\frac{1}{2^{2012}}\)
\(A=\frac{2^{2013}-1}{2^{2012}}\)
Vậy \(A=\frac{2^{2013}-1}{2^{2012}}\)
Đúng 0
Bình luận (0)
Rút gọn biểu thức:A=1+1/2 +1/22+1/23+...+1/22012
\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)
=>2A=\(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\)
=>2A-A=\(\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)=2-\frac{1}{2^{2012}}\)
=>A=\(\frac{2^{2013}-1}{2^{2012}}\)
Đúng 0
Bình luận (0)
Tính giá trị biểu thức:A=1/2+1/3+1/4+...+1/2014 phần 2013/1+2012/2+2011/3+...+1/2013
Giúp mk nha!!
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+...+\left(\frac{1}{2013}+1\right)+1}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{2014.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}\)\
\(A=\frac{1}{2014}\)
Đúng 2
Bình luận (0)
Rút gọn biểu thức:
a) (2x + 1)2 + (2x - 1)2 - 2(x - 3)2
b) (x - 1)2 - (3x + 2)2
c) (6x + 1)2 + (6x - 1)2 - 2(1 + 6x) (6x - 1)
Rút gọn biểu thức:
a) (2x + 1)2 + (2x - 1)2 - 2(x - 3)2
b) (x - 1)2 - (3x + 2)2
c) (6x + 1)2 + (6x - 1)2 - 2(1 + 6x) (6x - 1)
a: \(\left(2x+1\right)^2+\left(2x-1\right)^2-2\left(x-3\right)^2\)
\(=4x^2+4x+1+4x^2-4x+1-2\left(x^2-6x+9\right)\)
\(=8x^2+2-2x^2+12x-18\)
\(=6x^2+12x-16\)
b: \(\left(x-1\right)^2-\left(3x+2\right)^2\)
\(=x^2-2x+1-9x^2-12x-4\)
\(=-8x^2-14x-3\)
c: \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(6x+1\right)\left(6x-1\right)\)
\(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)
\(=\left(6x+1-6x+1\right)^2=2^2=4\)
Đúng 1
Bình luận (0)
rút gọn các biểu thức:
a) (x-2)2-(2x-1)2+(3x-1)(x-5)
b) (x-3)3-(x+3)(x2-3x+9)+(3x-1)(3x+1)
a: Ta có: \(\left(x-2\right)^2-\left(2x-1\right)^2+\left(3x-1\right)\left(x-5\right)\)
\(=x^2-4x+4-4x^2+4x-1+3x^2-15x-x+5\)
\(=-16x+8\)
b: Ta có: \(\left(x-3\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+\left(3x-1\right)\left(3x+1\right)\)
\(=x^3-9x^2+27x-27-x^3-27+9x^2-1\)
=27x-55
Đúng 1
Bình luận (0)
Bài 1: Khai triển hằng đẳng thức:
a, ( x - y + 2z )2
b, ( 2x-3 ). ( 2x+3 ) . ( 4x2+9 )
Bài 2: Rút gọn biểu thức:
a, ( 5x+2 ).( 2-5x ) - ( 3x+2 ).( 2x+5 )2
b, ( -2x-3 )2 + 2(2x+1).( 2x+5 ) + ( 2x+5 )2
Bài 1:
a, \(\left(x-y+2z\right)^2=x^2+y^2+4z^2-2xy-4yz+4zx\)
b, \(\left(2x-3\right)\left(2x+3\right)\left(4x^2+9\right)=\left(4x^2-9\right)\left(4x^2+9\right)=16x^4-81\)
Đúng 1
Bình luận (0)
Xem thêm câu trả lời
16 tháng 8 2021 lúc 21:28
Rút gọn biểu thức:
a) (x+1)2 + (x – 1)2 – 2(1 + x)(1 - x)
b) 2x(2x – 1)2 – 3x(x+3)(x – 3) – 4x(x+1)2
c) 3(x + 2)2 – (3x + 1)(x + 5) + (x + 5)2
a: Ta có: \(\left(x+1\right)^2+\left(x-1\right)^2-2\left(1+x\right)\left(1-x\right)\)
\(=\left(x+1\right)^2+2\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\)
\(=\left(x+1+x-1\right)^2\)
\(=4x^2\)
c: Ta có: \(3\left(x+2\right)^2-\left(3x+1\right)\left(x+5\right)+\left(x+5\right)^2\)
\(=3x^2+12x+12-3x^2-16x-5+x^2+10x+25\)
\(=x^2+6x+32\)
Đúng 1
Bình luận (0)