rút gọn biểu thức sau cho A = 1/2^1+1/2^2+1/2^3+....+1/2^99+1/2^100
tick ai nhanh đúng nhất
rút gọn biểu thức :13+23+...+993+1003
ai nhanh nhất tui tick đúng
Rút gọn:
a/ A=2^100-2^99+2^98-2^97+............+2^2-2
b/ B=3^100-3^99+3^98-3^97+..............+3^2-3+1
Ai nhanh nhất là đúng nhất mk tick cho
\(A=2^{100}-2^{99}+2^{98}-2^{97}+....+2^2-2\)
\(2A=2^{101}-2^{100}+2^{99}-2^{98}+....+2^3-2^2\)
\(2A+A=2^{101}-2\)
\(A=\frac{2^{101}-2}{3}\)
b) tương tự
\(B=\frac{3^{101}+1}{4}\)
Rút gọn biểu thức sau:
a) S =\(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^n}\)
b) A=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)
AI LÀM NHANH MÀ ĐÚNG MIK TICK
Rút gọn biểu thức: A = 1+ 1/2 + 1/2^2 + 1/2^3 + .....+ 1/1^2012
Ai nhanh mk tích
Rút gọn các biểu thức sau:
a) A = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^3}\) +...+ \(\dfrac{1}{3^n}\)
b) B = \(\dfrac{1}{2}\) - \(\dfrac{1}{2^2}\) + \(\dfrac{1}{2^3}\) - \(\dfrac{1}{2^4}\) +...+ \(\dfrac{1}{2^{99}}\) - \(\dfrac{1}{2^{100}}\)
c) C = \(\dfrac{3}{2^2}\) x \(\dfrac{8}{3^2}\) x \(\dfrac{15}{4^2}\) ... \(\dfrac{899}{30^2}\)
(Mình cần gấp ạ)
b, B = \(\dfrac{1}{2}\) - \(\dfrac{1}{2^2}\) + \(\dfrac{1}{2^3}\) - \(\dfrac{1}{2^4}\)+.....+ \(\dfrac{1}{2^{99}}\) - \(\dfrac{1}{2^{100}}\)
2 \(\times\) B = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\) - \(\dfrac{1}{2^3}\) + \(\dfrac{1}{2^4}\)-.......-\(\dfrac{1}{2^{99}}\)
2 \(\times\) B + B = 1 - \(\dfrac{1}{2^{100}}\)
3B = ( 1 - \(\dfrac{1}{2^{100}}\))
B = ( 1 - \(\dfrac{1}{2^{100}}\)) : 3
A = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\)+ \(\dfrac{1}{3^3}\)+......+ \(\dfrac{1}{3^{n-1}}\) + \(\dfrac{1}{3^n}\)
A\(\times\) 3 = 3 + 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^2}\)+....+ \(\dfrac{1}{3^{n-1}}\)
A \(\times\) 3 - A = 3 - \(\dfrac{1}{3^n}\)
2A = 3 - \(\dfrac{1}{3^n}\)
A = ( 3 - \(\dfrac{1}{3^n}\)) : 2
C = \(\dfrac{3}{2^2}\) \(\times\) \(\dfrac{8}{3^2}\) \(\times\) \(\dfrac{15}{4^2}\) \(\times\) ...........\(\times\) \(\dfrac{899}{30^2}\)
C = \(\dfrac{1\times3}{2^2}\) \(\times\) \(\dfrac{2\times4}{3^2}\) \(\times\) \(\dfrac{3\times5}{4^2}\) \(\times\)........\(\times\) \(\dfrac{29\times31}{30^2}\)
C = \(\dfrac{1\times2\times\left(3\times4\times5\times....\times29\right)^2\times30\times31}{2^2\times\left(3\times4\times5\times.......\times29\right)^2\times30^2}\)
C = \(\dfrac{2\times\left(3\times4\times5\times.....\times29\right)^2\times30}{2\times\left(3\times4\times5\times.....\times29\right)^2\times30}\) \(\times\) \(\dfrac{1\times31}{2\times30}\)
C = 1 \(\times\) \(\dfrac{31}{60}\)
C = \(\dfrac{31}{60}\)
a) Rút gọn biểu thức sau:
A=2*2^2+3*2^3+4*2^4+5*2^5+...+100*2^100
b) Cho B=1/2-1/3+1/4-1/5+...+1/98-1/99
CMR: 0,2< B < 0,4
Rút gọn các biểu thức sau:
a) A = 1+1/3^2+1/3^3+...+1/3^n
b) B = 1/2-1/2^2+1/2^3-1/2^4+...+1/2^99-1/2^100
c) C = 3/2^2 x 8/3^2 x 15/4^2 ... 899/30^2
A = 1 + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^3}\) +.......+\(\dfrac{1}{3^{n-1}}\) + \(\dfrac{1}{3^n}\)
3\(\times\) A = 3 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^3}\)+........+ \(\dfrac{1}{3^{n-1}}\)
3A - A = 3 + \(\dfrac{1}{3}\) - 1 - \(\dfrac{1}{3^n}\)
2A = \(\dfrac{7}{3}\) - \(\dfrac{1}{3^n}\)
A = ( \(\dfrac{7}{3}\) - \(\dfrac{1}{3^n}\)): 2
A = \(\dfrac{7.3^{n-1}-1}{3^n}\) : 2
A = \(\dfrac{7.3^{n-1}-1}{2.3^n}\)
B = \(\dfrac{1}{2}\) - \(\dfrac{1}{2^2}\) + \(\dfrac{1}{2^3}\) - \(\dfrac{1}{2^4}\)+......+\(\dfrac{1}{2^{99}}\) - \(\dfrac{1}{2^{100}}\)
2B = 2 - \(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\) - \(\dfrac{1}{2^3}\)+ \(\dfrac{1}{2^4}\)-.......-\(\dfrac{1}{2^{99}}\)
2B + B = 2 - \(\dfrac{1}{2^{100}}\)
3B = 2 - \(\dfrac{1}{2^{100}}\)
B = ( 2 - \(\dfrac{1}{2^{100}}\)): 3
B = \(\dfrac{2.2^{100}-1}{2^{100}}\) : 3
B = \(\dfrac{2^{101}-1}{3.2^{100}}\)
Rút gọn biểu thức sau :
\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
Ta xét biểu thức sau :
\(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n}+\sqrt{n+1}\right)}=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}\left[\left(\sqrt{n+1}\right)^2-\left(\sqrt{n}\right)^2\right]}\)
\(=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\)(với n > 0)
Áp dụng : \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
\(=\left(\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}\right)+\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\right)+...+\left(\frac{1}{\sqrt{99}}-\frac{1}{\sqrt{100}}\right)\)
\(=1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{99}}-\frac{1}{\sqrt{100}}=1-\frac{1}{\sqrt{100}}=1-\frac{1}{10}=\frac{9}{10}\)
Rút gọn các biểu thức sau:
a, | x2 + 2 | + | x2 + 1|
b, | 2x - 3 | + | 3x - 2 | ( với x > 2 )
c, | x - 4 | + | 5 - x | với 4 > x
d, | 1 - x2| - | 1 + x2| với x > 1
Giups mik với nhé. Mik sẽ tik điểm cho những ai làm bài nhanh và đúng nhất. Chân thành cảm ơn...........!
Nhanh nhé các bn, mai mik phải nộp r...huhu
a) | x2 + 2 | + | x2 + 1 | = x2 + 2 + x2 + 1 = 2x2 + 3
b) | 2x - 3 | + | 3x - 2 | = 2x - 3 + 3x - 2 = 5x - 5 = 5( x - 1 ) với x > 2
c) | x - 4 | + | 5 - x | = -( x - 4 ) + 5 - x = -x + 4 + 5 - x = -2x + 9 ( với 4 > x )
d) | 1 - x2 | - | 1 + x2 | = -( 1 - x2 ) - ( 1 + x2 ) = -1 + x2 - 1 - x2 = -2 ( với x > 1 )
a. Vì \(x^2\ge0\forall x\)
\(\Rightarrow\left|x^2+2\right|+\left|x^2+1\right|=x^2+2+x^2+1=2x^2+3\)
b. Vì \(x>2\)\(\Rightarrow2x-3>1;3x-2>4\)
\(\Rightarrow\left|2x-3\right|+\left|3x-2\right|=2x-3+3x-2=5x-5\)
c. Vì \(4>x\)\(\Rightarrow x-4< 0;5-x>1\)
\(\Rightarrow\left|x-4\right|+\left|5-x\right|=-x+4+5-x=-2x+9\)
d. Vì \(x>1\)\(\Rightarrow1-x^2< 0;1+x^2>2\)
\(\Rightarrow\left|1-x^2\right|+\left|1+x^2\right|=-x+x^2+1+x^2=2x^2-x+1\)