Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Giải:
A=1/22+1/32+1/42+...+1/92
Ta có:
1/22<1/1.2
1/32<1/2.3
1/42<1/3.4
...
1/92<1/8.9
⇒A<1/1.2+1/2.3+1/3.4+...+1/8.9
A<1/1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9
A<1/1-1/9
A<8/9
Ta có:
1/22>1/2.3
1/32>1/3.4
1/42>1/4.5
...
1/92>1/9.10
⇒A>1/2.3+1/3.4+1/4.5+...+1/9.10
A>1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10
A>1/2-1/10
A>2/5
Vậy 2/5<A<8/9 (đpcm)
Chúc bạn học tốt!
\(a,x-36:18=12-15\\ \Rightarrow x-2=-3\\ \Rightarrow x=-1\\ b,92-\left(17+x\right)=72\\ \Rightarrow17+x=20\\ \Rightarrow x=3\\ c,720:\left[41-\left(2x+5\right)\right]=40\\ \Rightarrow41-\left(2x+5\right)=18\\ \Rightarrow2x+5=23\\ \Rightarrow2x=18\\ \Rightarrow x=9\\ d,\left(x+2\right)^3-23=41\\ \Rightarrow\left(x+2\right)^3=64\\ \Rightarrow\left(x+2\right)^3=4^3\\ \Rightarrow x+2=4\\ \Rightarrow x=2\)
2:
1: =>36x+14x=69+81=150
=>50x=150
=>x=3
2: 3^x=81
=>3^x=3^4
=>x=4
3: 3(2x+1)^2=75
=>(2x+1)^2=25
=>2x+1=5 hoặc 2x+1=-5
=>x=-3 hoặc x=2
1:
1: \(\dfrac{13\cdot17^4+4\cdot17^4}{17^3}-\dfrac{14\cdot3^3-14\cdot3^2}{9}\)
\(=\dfrac{17^4\cdot\left(13+4\right)}{17^3}-\dfrac{14\cdot3^2\left(3-1\right)}{9}\)
\(=17\cdot17-14\cdot2\)
=289-28
=261
2:
\(2^3\cdot5^2-\left[131-\left(23-2^3\right)^2\right]\)
\(=8\cdot25-131+\left(-1\right)^2\)
=69+1
=70
A=1/2[(7^4)^2008^2015-(3^4)^88^94]
A=1/2.[(...1)-(...1)]
A=1/2.(...0) ma (...0) chia het cho 5 nen 1/2.(...0) chia het cho 5
nen A chia het cho 5.
Vay A chia het cho 5
A = ( -4/5 + 4/3 ) + (-5/4 + 14/5) - 7/3
= 8/15 + 31/20 - 7/3
= 25/12 - 7/3
= -1/4
B = 8/3 x 2/5 x 3/8 x 10x 19/92
= 16/15 x 15/4 x 19/92
= 4x19/92
= 19/23
C = - \(\dfrac{5}{7}\) x \(\dfrac{2}{11}\) + \(\dfrac{-5}{7}\) x \(\dfrac{9}{14}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{10}{77}\) - \(\dfrac{45}{98}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{635}{1078}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{36195}{61446}\) + \(\dfrac{1078}{61446}\)
= - \(\dfrac{35117}{61446}\)
\(A=\dfrac{17^{100}+17^{96}+17^{92}+....+17^4+1}{17^{102}+17^{100}+17^{98}+....+17^2+1}\)
Gọi \(17^{100}+17^{96}+17^{92}+....+17^4+1\) là B
\(B=17^{100}+17^{96}+17^{92}+....+17^4+1\\ 17^4\cdot B=17^{104}+17^{100}+17^{96}+......+17^8+17^4\\ 17^4\cdot B-B=\left(17^{104}+17^{100}+17^{96}+......+17^8+17^4\right)-\left(17^{100}+17^{96}+17^{92}+....+17^4+1\right)\\ B\cdot\left(17^4-1\right)=17^{104}-1\\ B=\dfrac{17^{104}-1}{17^4-1}\)
Gọi \(17^{102}+17^{100}+17^{98}+....+17^2+1\) là C
\(C=17^{102}+17^{100}+17^{98}+....+17^2+1\\ C\cdot17^2=17^{104}+17^{102}+17^{100}+17^{98}+....+17^2\\ C\cdot17^2-C=\left(17^{104}+17^{102}+17^{100}+17^{98}+....+17^2\right)-\left(17^{102}+17^{100}+17^{98}+....+17^2+1\right)\\ C\cdot\left(17^2-1\right)=17^{104}-1\\ C=\dfrac{17^{104}-1}{17^2-1}\)
=>
\(A=B:C\\ A=\dfrac{17^{104}-1}{17^4-1}:\dfrac{17^{104}-1}{17^2-1}\\ A=\dfrac{17^2-1}{17^4-1}\)
a) 58.57+58.150-58.125
=58.(57+150-125)
=58. 82
= 4756
b)32.5-22.7+83.20190
=9.5-4.7+83
=45-28+83
=100
c)2019+(-247)+(-53)-2019
=(2019-2019)+[ (-247)+(-53)]
0+(-300)
= -300
d)13.70-50 [(19-32):2+23]
=13.70-50[10:2+8]
=13.70-50.13
=13.(70-50)
=13.20
=260
2.
a)x-36:18=12-5
x-36:18=6
x-36=6.18
x-36=108
x=108+36
x= 144
b)92-(17+x)=72
17+x=92-72
17+x=20
x=20-17
x=3
c)720:[41-(2x+5)]=40
41-(2x+5)=720:40
41-(2x+5)= 18
2x+5=41-18
2x+5=23
2x=23-5
2x=18
x=18:2
x=9
d) (x+2)3 -23=41
(x+2)3 =41+23
(x+2)3 =64
=> (x+2)3 =43
=>x+2=4
=>x=4-2
=>x=2
Ta có: 74n+1 = ...7 => 74n = ...1. Mà 2012 chia hết cho 4 => 20122015 chia hết cho 4 => 20122015 = 4n với n = x
=> 720122015 = ...1
Lại có: 34n+1 = ...3 => 34n = ...1. Mà 92 chia hết cho 4 => 9294 chia hết cho 4 => 9294 = 4n với n = y
=> 39294 = ...1
=> A = 1/2 [...1 - ...1]
=> A = 1/2. ...0 = ...0
Vậy A chia hết cho 5
Mà 720122015 - 39294 \(\ge\)0
=> 1/2[720122015 - 39294] \(\ge\)0
Vậy A là số tự nhiên
Từ đó suy ra A là số tự nhiên chia hết cho 5
AI THẤY ĐÚNG ỦNG HỘ NHÉ
CẢM ƠN MN
SSH: ( 17 - 1 ) : 2 + 1 = 9
Tổng: ( 1 + 17 ) . 9 : 2 = 81
\(9^2=81\Rightarrow1+3+5+...+17=9^2\)
vì 1+3+5+...+17=81
mà 81=9^2
Từ 2 điều trên =>1+3+5+...+17=9^2