NP
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Khách
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NN
2
5 tháng 2 2022
A = \(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)\)\(...\left(1+\frac{1}{2499}\right)\)
A = \(\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{8}{8}+\frac{1}{8}\right)\left(\frac{15}{15}+\frac{1}{15}\right)\)\(...\left(\frac{2499}{2499}+\frac{1}{2499}\right)\)
A = \(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{2500}{2499}\)
A = \(\frac{4.9.16.....2500}{3.8.15.....2499}\)
A = \(\frac{\left(2.2\right)\left(3.3\right)\left(4.4\right)...\left(50.50\right)}{3.8.15.24.....2499}\)
A = \(\frac{2.3.4.....50}{3.4.5.6.....51}\)
A = \(\frac{2}{51}\)
Vậy A = \(\frac{2}{51}\)
( Nếu sai mong bạn thông cảm ạ ! )
_HT_
YN
5 tháng 2 2022
Answer:
\(A=\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)...\left(1+\frac{1}{2499}\right)\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}...\frac{2500}{2499}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)
\(=\frac{2^2.3^2.4^2...50^2}{1.3.2.4.3.5...49.51}\)
\(=\frac{2.50}{51}\)
\(=\frac{100}{51}\)
14 tháng 1
\(A=\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)\cdot...\left(1+\dfrac{1}{2499}\right)\)
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot...\cdot\dfrac{2500}{2499}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot...\cdot\dfrac{50\cdot50}{49\cdot51}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot50}{1\cdot2\cdot3\cdot...\cdot49}\cdot\dfrac{2\cdot3\cdot...\cdot50}{3\cdot4\cdot...\cdot51}\)
\(=\dfrac{50}{1}\cdot\dfrac{2}{51}=\dfrac{100}{51}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
8 tháng 4 2023
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 = \(\dfrac{7.3^{n-1}-1}{2.3^n}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
8 tháng 4 2023
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 = \(\dfrac{2^{101}-1}{3.2^{100}}\)
C
1
10 tháng 1 2022
\(a,A=\dfrac{x^2-x-2}{x^2-1}+\dfrac{1}{x-1}-\dfrac{1}{x+1}\)
\(\Rightarrow A=\dfrac{x^2-x-2}{\left(x-1\right)\left(x+1\right)}+\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}-\dfrac{x-1}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{x^2-x-2x+x+1-x+1}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{x^2-3x+2}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{x^2-2x-x+2}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{x\left(x-2\right)-\left(x-2\right)}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{\left(x-1\right)\left(x-2\right)}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow A=\dfrac{x-2}{x+1}\)
\(b,A=\dfrac{3}{4}\\ \Rightarrow\dfrac{x-2}{x+1}=\dfrac{3}{4}\\ \Rightarrow4\left(x-2\right)=3\left(x+1\right)\\ \Rightarrow4x-8=3x+3\\ \Rightarrow4x-8-3x-3=0\\ \Rightarrow x-11=0\\ \Rightarrow x=11\)
\(c,\left|x-3\right|=2\Rightarrow\left[{}\begin{matrix}x-3=2\\x-3=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)
Thay x=5 vào A ta có:
\(A=\dfrac{x-2}{x+1}=\dfrac{5-2}{5+1}=\dfrac{3}{6}=\dfrac{1}{2}\)
Thay x=1 vào A ta có:
\(A=\dfrac{x-2}{x+1}=\dfrac{1-2}{1+1}=\dfrac{-1}{2}\)
LB
1
26 tháng 3 2022
Tính từng phép tính trong ngoặc ta được :
\(A= \frac{3}{4}. \frac{8}{9} . ....\frac{899}{900}\)
\(A=\frac{1.3}{2.2} .\frac{2.4}{3.3}.... \frac{29.31}{30.30}\)
Gộp các thừa số với sau được
\(A= \frac{(1.2.3.4....29)(3.4.5.6...31)}{(2.3.4...30)(2.3.4..30)}\)
\(A= \frac{31}{30.2} = \frac{31}{60}\)
13 tháng 5 2015
1:
I2x+3I = 5
=> 2x+3 = 5 hoặc 2x+3 = -5
=> 2x = 5 - 3 hoặc 2x = -5 - 3
=> 2x = 2 hoặc 2x = -8
=> x = 2 hoặc x = -4
2:
B = 1/2.2/3.3/4.4/5.....27/28
= 1.2.3.4.5.6...27/2.3.4.5.6...28
= 1/28
3:
2A = 2(1+1/2+1/2^2+1/2^3+1/2^4+...+1/2^2015) = 2+1+1/2+1/2^2+1/2^3+...+1/2^2014
=> 2A-A = ( 2+1+1/2+1/2^2+1/2^3+...+1/2^2014)-(1+1/2+1/2^2+1/2^3+...+1/2^2015)
=> A = 2-1/2^2015
LT
0
giúp mình nhanh nhé mình đang cần gấp.