D = 1/5 + 1/25 +...+ 1/3125
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
bài 6: TÍNH NHANH NÂNG CAO LỚP 5
A= 1/5+1/25+1/125+1/625+1/3125
giải hộ mình nhanh nhanh nha các bạn
5A=(1/5+1/25+1/125+1/625+1/3125)*5
5A=(1+1/5+1/25+1/125+1/625)
5A-A=(1+1/5+1/25+1/125+1/625)-(1/5+1/25+1/125+1/625+1/3125)=1-1/3125
4A=1-1/3125=3124/3125
A=3124/3125:4=781/3125.
\(\dfrac{1}{25}\)+\(\dfrac{1}{625}\)+\(\dfrac{1}{3125}\)=\(\dfrac{125}{3125}\)+\(\dfrac{5}{3125}\)+\(\dfrac{1}{3125}\)
=\(\dfrac{131}{3125}\)
chúc bạn học tốt ạ
a) \(2^n:4=16\Rightarrow2^n:2^2=2^4\Rightarrow2^{n-2}=2^4\Rightarrow n-2=4\Rightarrow n=6\)
b) \(6\cdot2^n+3\cdot2^n=9\cdot2^9\)
=> \(\left(6+3\right)\cdot2^n=9\cdot2^9\)
=> \(9\cdot2^n=9\cdot2^9\Rightarrow n=9\)
c) \(3^n:3^2=243\)
=> \(3^{n-2}=3^5\)
=> n - 2 = 5 => n = 7
d) 25 < 5n < 3125
=> 52 < 5n < 55
=> n \(\in\){3;4}
A = 3/1×5 + 3/5×9 + 1/9×13 + ... + 9/97×101 + 3/101×105
A = 3/4 × (4/1×5 + 4/5×9 + 4/9×13 + ... + 4/97×101 + 4/101×105)
A = 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101 + 1/101 - 1/105)
A = 3/4 × (1 - 1/105)
A = 3/4 × 104/105
A = 26/35
B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625
5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125
5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)
4B = 1 - 1/15625
4B = 15624/15625
B = 15624/15625 : 4
B = 3906/15625
C = 1 + 2 + 4 + 8 + 16 + ... + 2048 + 4096
2C = 2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192
2C - C = (2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192) - (1 + 2 + 4 + 8 + ... + 2048 + 4096)
B = 8192 - 1
B = 8191
Ta có:
a)\(25< 2^x< 3125\)
\(\Rightarrow2^4< 2^x< 2^{12}\)
\(\Rightarrow4< x< 12\)
b)\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=7450\)
\(\Rightarrow100x+5050=7450\Rightarrow10x=2400\Rightarrow x=240\)
c)\(1+2+3+..+x=\frac{x\left(x+1\right)}{2}=78.\)
\(\Rightarrow x\left(x+1\right)=156\)\(\Rightarrow x=12\)
d)\(12x+13x=25x=2000\Rightarrow x=80\)
e)\(6x+4x=10x=2010\Rightarrow x=201\)
Bài 1:
a) \(\dfrac{10^6\times10^2}{1000^3}=\dfrac{10^{6+2}}{\left(10^3\right)^3}=\dfrac{10^8}{10^9}=\dfrac{1}{10}\)
b)\(\dfrac{625^2\times57\times3125}{25}=\dfrac{\left(5^4\right)^2\times5^5\times57}{5^2}=\dfrac{5^{13}\times57}{5^2}=5^{11}\times57\)
Bài 2 :
a) (x - 5)5 = (x - 5)10
⇒ x - 5 = 0 hoặc x - 5 = 1
⇒ x ∈ {5 ; 6}
a) 52x . 5 = 3125
52x + 1 = 55
\(\Rightarrow\)2x + 1 = 5
\(\Rightarrow\)2x = 5 - 1 = 4
\(\Rightarrow\)x = 4 : 2 = 2
b) 5x + 5x + 3 = 630
5x + 5x . 53 = 630
5x . ( 1 + 53 ) = 630
5x . 126 = 630
5x = 630 : 126
5x = 5
\(\Rightarrow\)x = 5
c) 32x + 1 = 243
32x + 1 = 35
\(\Rightarrow\)2x + 1 = 5
\(\Rightarrow\)2x = 5 - 1 = 4
\(\Rightarrow\)x = 4 : 2 = 2
d) 32x + 1 = 9
32x + 1 = 32
\(\Rightarrow\)2x + 1 = 2
\(\Rightarrow\)2x = 2 - 1 = 1
\(\Rightarrow\)x = 1 : 2 = \(\frac{1}{2}\)
a) 5^2x.5=3135
=> 5^2x =3125:5
=> 5^2x =625
=> 5^2x = 5^4
=> 2x =4
=> x =4:2
=> x =2
Vậy x=2
781/3125